Very deep 5/10 overpair

[Kala1928]

If OP has not been reraising generally and especially against the other deep stack I would much rather reraise him light for a while before playing a reraised pot vs utg open with QQ with these stacks. Playing the first reraised pot with 300bb stacks and QQ against UTG seems like a spot where hero is going to end up in a veeery tough spot somewhere along the hand, and the pot will be bloated.
Raise the turn. There is very little value left on the river if you just call turn because villain isn't going to 3barrel with air or Jx often enough(on a non-J river) and he will simply c/f on the river to your valuebet.
As played check is fine, you could try 1/2-2/3 pot for value unless villain is supertricky and will make it 3k often knowing you propably dont have a J. You might feel stupid after checking it down with such a "strong hand".

Also, dont call a 3bet on the turn. Unless you feel like floating and shoving some rivers as bluffs/rebluffs.