Isolate pre for dead money (although I don't hate calling sometimes depending on feel for game), like flop sizing as played, but jam turn

Wait - the FLOP shove is a bad idea...

Because with 100 in the pot
and OP having 175 behind
he should only shove with JJ
but NOT with a set

now THAT makes a whole lot of sense.

This board has both a straight draw AND a flush draw
Because I don't see this set as nutted as you do
I think charging for draws to be the best way to get value for your hand
A 1/2 pot bet is way too small
a shove may be way too big... but with a drunk lagtard in the equation, I don't think it should be out of the question (or horrible advice)
I've seen them call with much worse hoping to hit something
guys on winner's tilt don't mind shoveling chips to the middle for the thrill of seeing if they'll win