Ah man, what a ballache. Here's the inside of my one, it's defo PCB mounted:
To be honest, the hardest part is getting the fucking PCB out; you have to bend things in certain ways, it too me literally an hour or so when I replaced the LED in mine. After that, replacing a pot will feel like a holiday.
Rather than opening it up and dicking around with the pcb, would it be easier to make something that can still turn the shaft and render the remains of that pot usable? I'm thinking of sugru or something here, but I've seen decent results achieved with a curtain hook before.
Do still have the bit that broke off? Might be worth trying gluing the shaft back on with some strong superglue. Won't be perfect but would work, as long as you don't get glue around the washer and gunk it up.
All good suggestions - even desoldering the original once the board was out would be a really dangerous job. PCBs like that really aren't designed to have parts removed.