If the "lightest nudge" is all it takes to restore power, then another approach is to increase the inertia (weight) of the mechanical flywheel.
This has been discussed before and the analysis is pretty nerdy, but if you're looking to coast thru track power interruptions, you're better off storing energy mechanically (vs. electrically). That is, a capacitor's stored energy has to be converted to mechanical energy via the motor which has conversion losses as well as energy needed to run the motor drive electronics. OTOH, the flywheel stores energy in directly usable form as mechanical momentum to advance the locomotive in the absence of track power.
So if looking for ideas outside the capacitor box you'll find interesting online discussions of modifying flywheels - for example using tungsten instead of brass as tungsten is more than twice as heavy.
Practically speaking I don't expect many guys have the ability to work with tungsten and/or to fabricate their own flywheels. But OGR being a discussion forum to, uhh, discuss ideas... on a rainy afternoon with nothing else to do, attach coins (half dollars or whatever) to the existing flywheel. This is just an experiment as you may not have the clearance to put the engine "shell" back on. Again, the "math" is pretty nerdy but if the added flywheel momentum works, one can then ballpark the size of capacitor needed if that's where you want to store the reserve energy. That is, most guys also don't have the size/type of capacitors needed just lying around...much less the comfort level tapping in to the motor electronics risking the dreaded release of magic smoke.