Well thank you for calling us experienced.
I commend you for betting your Jacks in that spot, it does take guts.
I would have tried to show it down or check-call for the following reasons:
1. you have poor relative hand strength.
2. The board is terrible for your hand, it just kept getting worse and worse.
3. you have poor position.
4. This is not heads up, this is 4 way.
5. you can't call a raise.
6. if anyone calls your bet, you have poor equity versus their calling range, in my opinion. you seem to disagree with this last point because you discount the possibility of an opponent holding an Ace or a Q more so than I do. That is a judgment call. It is not something that is always right or always wrong.
Good luck at the tables,
Magnum