I will tackle some of your questions that I feel I know the answer to.
Old epsom salts should be fine. It is just a mineral (magnesium sulphate). Check you didn’t get some fancy stuff with weird extras added in that might be an issue.
Yes just soaking is OK - sometimes even for bad cases. You could skip bandaging until you are back.
The key is repeated soaking to soften everything up. As often as you can for as long as you can.
While your partner is in town make sure he gets something that can create the ring to take the pressure off the bumble once you start bandaging. @bgmathteach uses corn rings from the foot care part of the pharmacy. That foam that is used to insulate plumbing pipes is also good (you cut off slices).
Also he should get whatever drawing salve is available in France. The gold standard would be anything containing ichthammol.
And lots of vetwrap bandage because it sticks to itself.

@ManueB I can add that bumblefoot, from what I have read and from others experience or suspicions is that common causes are repeated landings on a hard surface, like a concrete coop floor (I picture it as the foot hitting a tiny pebble or rock, but it doesn’t give because the surface beneath is hard so the flesh is injured, it but it might be a repeated bruising that goes bad internally). Or something sharp cutting or puncturing the foot like what you are fearing, sharp edges, but it can be splinters or thorns (wild roses or brambles in the case of @Kris5902). Do you see your birds using the ramp or jumping right off?
Some people use a series of small steps instead, as you suggest. I’d use at least two with the height you have.
If you are concerned about the screws on the ramp steps, since they aren’t countersunk deeply, maybe that could be a cause. Do the screws go through all the wood and stick out the other side? If not, remove them, and screw them back in to the steps from the back side. That way there’ll be no heads on the upper side.
Before you do that though, either sand and smooth all the corner edges, or get wood lengths that are easier to smooth. Young tree branches might work (the smooth lengths between branching), or if you can buy a split dowel, that would be great because it’s a half-round shape and will sit flush on the ramp.