Yes I know about those solutions, this is why I specifically asked if a simplier all in one hardware solution exists.
Even the MOTU Ultralite won't tick your boxes. You're probably not going to find a hardware switch solution for muting the outputs when plugging in headphones. I can't even think of an interface that has some plug detection mechanism.
I wouldn't recommend a software solution for you either. I do use a thunderbolt interface with software FX and I can get 6ms round trip latency, which is good enough for realtime, and does everything you could want, but it's not a "one button - everything on" solution, not to mention pricey.
The best idea is to split the FX from the interface. Plenty of interfaces have compression but not de essers that I can think of. A separate multi-fx unit will provide "realtime" FX, and provide enough flexibility with tonal shaping. Even if you found a all-in-one solution, you would probably find the tonal control to be lacking, hence why it's better to go for a dedicated FX unit. When you get really fussy, even the multi-FX are a compromise and you get individual FX!
A vocal specific rack unit would probably be the best starting point, one with compression and de essing, something like a dbx 286 or similar brand. You could either plug the XLR mic directly into the unit, then route from the rack unit to the interface, or run an FX loop from an interface with enough ins/outs.
Some of the more modern interfaces, take MOTU for example, use a web based interface for mix control and allow for more flexible remote control of volume and other parameters. You may be able to work out an easy mute/unmute system for your outputs.
So lastly your DIY suggestion.....probably the least efficient way unless you're making it for the purpose of your own edification, or your required solution is really, really specific (which it isn't, the interface + vocal rack unit will work). Check out this project involving multi fx based around a pi:
https://www.treefallsound.com/It's on my list of things to do.
By the way I don't understand not wanting to combine units. Everything you're asking for will fit into a 2 rack unit case, you can have it all connected in the case and will require minimal setup time if you move the case around.