Probably like Dave, but I just remap mame to use multi-button combos, and forget (in fact, disable if possible) shift feature. (Forget joy2key, too.)
IMO, the first step is to stop thinking "tab", "enter", "esc", etc, and instead what they
do and are called in mame: "Config Menu", "UI Select", and "UI Cancel" ("exit"). Which just happen to be mapped to those respective keys by default. Then map these "newly named" but same functions to whatever key/button/(s) you want. For example, IMO "UI Select" should be mapped to whatever is p1b1 and/or p2b1, instead of adding another button to the CP.
This is weighted toward mame/mess, though; other games/emus might need keypresses or can't remap to multi-button per action.

Possible actions:
- Remap mame, including dual and triple button presses.
- Remap mame, including shifted buttons and dual and triple buttons presses.
- Remap/rewire encoder to match mame's defaults, one key per. (only works for keyboard encoders if you want mame's default admin buttons)
- Remap encoder to match mame's default, using shift key (only works for keyboard encoders)
- Use joy2key or similar app to convert joy signal to key presses. IMO, adds extra steps, increases input latency, and app needs to be RawInput aware to work with mame. IOW, IMO a PITA. However, needed for some non-mame emus not currently upkept.
- Some combo of the above
You're used to the #3 & #4 with the ipac, but with the u360 they aren't options any more. I prefer the first one, ipac or u360, and IMO #5 should be the last course.