My idea was to put a microcontroller in each module in I2C slave mode.
I have done that in several designs; however always on the same board

This micro reads / debounces the switches and sends the status to the main controller when asked.
This is about every 50ms
Good ides, just add an interrupt line (just a port pin resistive pulled up so the slaves can say "I have something for you"

When using a second UART the best thing to do would be to use RS485 with a simple protocol. Figuring out where to put the terminations is the next step. Since 1 or two modules can be connected to the main unit the terminations have to be switchable.
if the units are close enough, you can use just a wired or, no 485 drivers needed

I2C seems a lot easier.
that is what I would use if the capacitance is low enough, I would not go UART if sigle wire is feasible.

A sufficiently slow IIC or wire-ored UART could go 1000 miles were there no (stray, component, ...) capacitance on the bus

Erik