Love the pic.
That switch might very well be the problem. I have a similar switch with my thermocouples and it introduced a significant error, similar to yours.
A thermocouple is made of 2 dissimilar metals that generate a small voltage that changes with temperature. If you introduce other metals (i.e., your switch), you get errors.
The best solution is to change to RTDs or thermistors. You need to make sure your PID supports that first. And, of course, it will get you and your friend busy swapping them out. Not a picnic. I didn't do that either
What I did was get my mash BK to about normal strike temp (165F), measured with a good thermometer, then I adjusted the offset in my PID. I think I was off by about 3F.
Now my PID reads correctly at 165F. When I'm boiling, it reads about 210, which is of by 2 but I really don't care as long as it's boiling.
BTW, I had a much bigger problem with heat in my box. I moved my heat sinks outside the box and that made a big difference as well. This is also a problem specific to the use of thermocouples.