I play 1/2 and for me 4! is KK+ almost always.
I agree his line is a bit suspect. V might have taken it personally when you were c betting him off the flop. Maybe this is a spaz getting you back move. You're in very dangerous territory nearly 400bb deep though.
Going through the options:
1) Fold - I like folding generally and here specifically
You're up, nearly going home and so far only put $75 in this pot so why not just take the easy way out right now?
2) Call $125 and assess flop: You do have odds to set-mine, not 20:1 maybe but pot is $275 and V has $1700 behind so it is 1975:125 implied plus pot odds. Trouble is what are you doing the 40% of the time you flop an overpair? I'm happy set mining but really worry about continuing without a set.
3) 5!/fold to $400: I'm not loving this considering you can set-mine and this is just turning a hand with no blockers into a bluff. What if villain ships AK (or worse AX???) and you fold? That's a nearly 100bb folding error I'm keen to avoid making.
Overall I just don't think you have sufficient info on this villain to take JJ postflop OOP and play poker. Similarly not enough info to 5!/fold and if you had info on hiw he plays calling is probably better anyway.
Set-mine > fold > call and play poker postflop > 5!/F
That's my humble and quite possibly wrong opinion. I like to test myself by being first in though so let's see what everyone else thinks...