The Sidebar plugin actually solves this in a very nice way, should have looked at this first.
In this mockup the expanded extruder panels could have a minimum width, at some point being wider, but 90% of Users probably have <2 Extruders.
In Custom Mode the right panel could be for choosing a profile with the print settings always being shown in the Background (not as floating window) like this:
Choosing a printer, material, and profile whould be visually on the same hierarchical level, and print settings below that, being a result of these choices.