For legacy EX products, you can upgrade directly from any 12.3 to any 15.1. There is no need, nor any good reason, to go to either 13.x or 14.x for these products.
I have never used J-Web to upgrade, but I do know that upgrades via either CLI or Space (Platform or ND) do work. My only suggestion is to try this via CLI for some switch or group of switches. I am also not sure how you are actually performing the upgrade, be it standard method or something like NSSU. I am actually not sure what options J-Web may have.
Good luck