If you do want to pursue human vs human conflict, Phoenix Point is planning to explore that in a big way. So probably some good ideas to take from there.
Seems like it might be a bit too easy outside a videogame though. When you say “can’t we put this issue aside until we save the Earth”, it is going to be harder to take the character seriously when they say no…
If you base it off of BoB the individual soldiers don’t really have downtime actions. It’s the Quarternaster that decides on downtime I think? I’ve only listened to the game as podcasts 
That said, there are labourers in BoB that I think function as your extra downtime. You could just use that unchanged. You need a lot of people to run a resistance after all.
The officers for an XCOM style game would obviously (I think) be the engineer, the scientist, and the mission control officer.
The GM gets to be the faceless guy on the screen 
You might have to be a little creative, but given human nature it’s inevitable that there’s animosity between them, even during an alien occupation.
As to human conflict, this kind of drama often includes a B-Plot that covers internal conflict. “Why couldn’t this wait” isn’t likely to be used as an excuse when the questions being asked are “who will lead the insurgency?” or “are these methods moral?”
As to downtime: I personally am a big fan of focusing on downtime as narrative beats. Following a single soldier during downtime or solo recon missions is an opportunity to add personal drama to the game.
On that note: personal recon missions that take a single soldier out of the action temporarily could be a good replacement for Secondary missions, information gathering, OR long term projects. Maybe all of the above?
Perhaps cohorts could be something like Cells? Groups of other operatives that have their own strengths and weaknesses, which accomplish goals for the insurgents, but can get wrecked and change over time, similar to player traumas? Becoming more radical, aggressive, or demoralized, creating conflict within the insurgency.
There’s a lot of cool shit you could do with this, and I could almost write up a draft of a possible game structure. Only problem is what mechanics to use.
BoB is better for a slightly larger scale game, the player takes on the roles of the Commander, Chief Engineer and Head Scientist during downtime, while the troops get screen time on missions and in downtime scenes.
There’s a lot of obvious (to me) resources to play with. Imo regional faction reputation should be important. Maybe only regions you have positive status with contributes funds to your organization, and mission outcomes and Entanglements modify them up and down.
To make levelling more militaristic, and simpler to manage if you have many soldiers and operatives to keep track of, you could have upgrades in the form of Promotions (8 XP, playbook advancement) and Medals (6 XP, attribute increase).
Just track one XP value per soldier.
Want to buy that Marksmanship Medal for the sniper or do you hold off to get promoted instead? 
Fictionally the Medals are recognition for skills the soldier has already developed, and Promotions are extra training and equipment to get new abilities.
Liking these ideas.
On base building: I feel the base building element would take the place of BoB’s Chosen. The different upgrades would be like advancements tied to a new room or facility.
I think progression is an interesting area.
I almost might recommend going with a Burning Wheel style trait vote every once in a while, where the players, playing the command staff a la BoB, vote on promotions and medals rather having them earned with experience points. Promotions typically bring more responsibility and authority, not more skill, and a marksmanship badge is, as you say, to recognize achievements.
Brainstormed some faction ideas last night, since this idea won’t get out of my head it seems. Names are placeholders and often just point to where the idea came from.
Collaborators
Humans who choose to side with the alien invaders.
Transitional Authority/Puppet Government - Those who rule the human colonies, safe zones, and cities in the name of the alien invaders.
Civil Protection/Homeland Security - Boots on the ground, the military arm of the transitional government who enforce their laws with brutal authority.
The Corporation - This company works with the aliens to make products and jobs that make the alien’s lives and the occupation easier, hoping to receive the secrets of advanced alien tech in return.
Influencers - Those who buy into and distribute alien propaganda.
Thin Men/Men in Black - Alien hybrids or early human collaborators that can blend into human populations and spy on the resistance. Maybe they’ve been doing this for a very long time, prepping the world for invasion.
Aliens
The invaders who occupy the earth
The Conclave/Fleet Command - Top of the alien food chain, who rule all alien interests far removed from Earth. They manage their empire from another dimension/distant space/another time.
Alien Generals/Commanders - The few key players that hunt insurgents, lead the alien military, and oversee projects on Earth (each a separate faction, or leads a separate faction?)
Alien Shock Troops - first line of invasion and defense for the aliens. Serve as bodyguards for VIPs on Earth
Drone Swarm - Robots and machines of alien design that help hunt insurgents and keep the peace (may or may not have sentience).
Xeno Beasts - Creatures of alien origin. A minor hindrance or pet for the aliens, but a deadly predator for us. Swarm throughout unprotected areas on earth (they mostly come out at night, mostly).
The Resistance
Those who fight back
Pirate Radio - Artists and speechwriters who spread messages of hope, constantly on the move to evade capture.
Radicals - Resistance fighters who are unconcerned with human collateral damage in their pursuit of the aliens and their collaborators.
Clinics/Doctors - Those who treat wounded resistance members, diseases the occupation deems unfit to address, and alien physiology when they can.
Xeno Rebels - Aliens who rebelled against the occupation and try to work with insurgents to fight back
Survivalists - People who fled the cities or survived the alien occupation by retreating to the wilderness or the abandoned suburban sprawl outside the city.
Spooks - Remnants of intelligence agencies and spies from the world before the invasion, trying to organize an insurgency that sees the old status quo re-established.
Those are good. Might be worthwhile looking at https://en.m.wikipedia.org/wiki/McCormick_Magic_Diamond
I was introduced to it via sigmata. It’s a good model of organizational relationships in a COIN setting, and how both the occupier and insurgents try to attack and disrupt each other’s relationships.
This is spookily similar to something I’ve been working on! The link to the google doc is here if anyone would like to see if there are useful insights to salvage:
I just skimmed it, but it looks cool so far 
This is a very cool start - although I wonder if having six “default” stations is too much for a BoB hack, they’re almost always going to end up being split between less players.
My thinking was that rather than the required/optional split that Bob uses, all six positions are 'core but split up as much as possible, with the expectation that they will be combined in typical groups. It is after all easier to give one person two playsheets than split responsibility for one playsheet between two players. The final version will have suggested combinations (for example, biomedical and science will usually go together in a 5 player group).
https://drive.google.com/drive/folders/1YdCPvI1rN7yED0QZHTzSQUo-UvWjac3U?usp=sharing
If anyone is interested, my attempt at hacking Band of Blades/Blades in the Dark to run something like X-Com 2 meets Half Life 2 is playtest ready.
I really like this. The playbooks gave good flavor, but the cadre leader took me a while to realize that it was a “rookie” type character. I love the q branch special ability.
I need more time to process the section sheets, but they look good. Having the GM spend threat to disrupt the resistance should work well to drive play.
This is a pretty cool model for any type of resistance.
I really like what I’m seeing here, Ranx, and it seems to be a pretty faithful and straight forward adaption of some of the tropes.
Thank you!
I’m fairly dissatisfied with the name ‘Cadre Leader’, it’s not euphonic and also the playbook should allow people to play as actual rookies rather than having to be leaders. the playbook was originally called just ‘Cadre’ but that caused all sorts of confusion. I’d welcome suggestions along those lines!
(and any other suggestions of course)
Thank you!
Rookie, grunt, combatant, green, soldier (since the others are all specialists), Cherry, Noob, Fodder, FNG (F’n New Guy)