I think you’re on the right track here. A big part of this system is choosing which mechanics to use to represent the fiction best – and which are going to be the most fun for the table.
I think a clock would be great for this. Give it a cool name, and bring it into play when it makes sense in the fiction. It can be obvious (the crew is messing with a ritual cast by the same cult, which energizes the body-altering flesh inside them), or it can surprise everyone at the table including you (“You get electrocuted by touching the lightning wall, aaaaand – Oh! I think the desperate consequence is that the electroplasmic discharge wakes that god-flesh you ate way back when… You feel this rending pain as it expands inside you – and you stare in horror as you grow a strange vestigial limb under your right arm. 3 ticks on that clock. Or do you want to resist that?”).
Changes to that fiction and clock can happen due to consequences, fictional occurrences, master-level npc actions, Devil’s Bargains and so on. Often (usually, I’d say), these moments will allow the players a chance to resist or decline if they want to. Something like this might be quickly played out, or it could become the slow-burn throughline of a campaign.
In the Blades rules as written, it’s specifically stated that clocks are meant to be seen as gauges that measure the progress of the fiction but don’t dictate it. (Fiction First) So when the character grows an extra arm, and we see that 4 of 8 segments of the clock are filled, we the players know that while it looks grim right now, there are worse things to come. There is also time to stop it.
Personally, I find it helpful to think of the idea that clocks can be both prescriptive and descriptive (a concept regarding mechanics in Dungeon World) for the gm. This is not an idea stated in Blades, and may be a little heretical to offer up here. But what I mean is: if you’re staring at the dice, which say that there’s a Risky consequence, and there’s a six-clock on the table with 3 ticks filled, you can decide mechanically to add 2 ticks to it. There are rules to this game, and they are legitimate aids to our fiction/story-making. The trick is that then you need to let yourself be inspired by that shift. Change the fiction to reflect it. The situation gets much more dire. Everything hangs on the precipice. Describe it. Make it real. Then change the clock.
As to what the fictional changes are – you might be totally inspired with cool ideas, or you might ask your table. I’ve had players pitch really twisted and interesting stuff at me for things like this, which I immediately added into the story. These moments can be great opportunities to discover what you as a group are interested in finding through play. (Your players had their characters consume this flesh. It seems like they’ve bought in to this story and its potential consequences.)
Your job as gm is then to realistically portray the world. A bunch of monstrous PCs sprouting extra limbs will definitely change how people react to them. The Lampblacks stop dealing with you because they think you’re freaks? Lynch mobs appear as a consequence to a botched roll? Reduced position on that important Consort roll? A Devil’s Bargain that the Spirit Warden will see your supernatural limb under your cloak? Let the world react, then let the players find ways to overcome that stuff. Disguises? Developing a ritual or concoction to reverse the transformation? Slipping metamorphosis flesh into the food supply so everyone ends up that way? Now it’s getting fun!