Backfires and runs roughly

After sitting for a couple of years, the vehicle ran smoothly for a month and then began backfiring and running very badly in low speeds and takeoff. Seemed like lost power. Runs ok at higher speeds (45+). In traffic, very sluggish on restart and backfires, jumps many times under load.

Mechanic says there is an anti-backfire regulator that has broken into several pieces. I have not seen it but he says he can not find the part anywhere and has even replaced the exhaust manifold in hopes the piece would be fixed. Seems to be the same issue with no improvement.

I hate to get rid of it but if it can not be repaired, no use to have it.

Do you have suggestions as to whether this can be repaired?