Am I missing something here? You don't nees to use a fet in the linear region here

the only problem that OP pointed out was the contacts welding due to inrush current, so I assume the circuit itself is fine with that

I had a similar issue for a project (only suitable size switches (8x8mm latching switches) were rated for 100s of mA but I needed 1.5A) and just used the switch to turn on the fet (i.e. short out gate to GND since I was using a P channel fet and a 10K pullup resistor to source) you can use an N channel fet with a pulldown resistor and a switch to connect it to VCC. Then the fer carries all the current wich would be fine, and the switch no longer welds itself since it carries no real amount of power

if the entire circuit requires inrush current limiting, then this would not work.
Edit: if you decide to switch the AC mains, you can still do the same with a triac rather than fets.just be sure to include an optocoupler since it's not wise to have your switch controll actual AC unless it's fused and tested for safety (i.e: not cheap chinese crap) but I would still use an optocoupler even with a proper switch just to be extra safe
