Sorry, it's not the power source if your strat is worse ... it's just life with single coil pickups.
I am not familiar with the Tribute's electronics and don't know if there is any hum balance control. But generally in these situations you want to be physically far away from the offending transmitter (dimmer packs), find the quietest spot in the band's area to set up, search for the best orientation and aim your instrument in that quiet direction for the soft musical passages. I know, not ideal, but it's what we do.
Or you could work on the source of the problem and try to convince the church to install a true Variac dimmer!
Good luck,
JJ