I'm not folding the top of our range vs a limper who is less likely to have AK/AA in this spot, might be doing this with worse FHs or even some Qx here. Turn needs to be way bigger considering villain is likely calling inelastic.

This is a mandatory shove vs a fish. He very likely has a bare Q and will stack off. I know you're 250 ish bb deep so it sucks the rare times he happens to have AA or AK, but imo not shoving for value would be criminal.

First of all you need to bet bigger. At least on the turn. J will certainly help him in some way, and because of that he is more likely to call you.
On the river I'm shoving as well. Versus a fish, who could be doing that with Q it's mandatory to do so. The only hands that are beating you are: 3 combos of AA, and 3 combos of AK. Also it's very unlikely that he would have those hands considering the fact, that he only limped/call pre.