That's a tough situation, and you (or rather your band mates) probably won't like my recommendation for fixing it. But here it is anyway...
Buy a couple of DPA 4099 mini condenser mics with one guitar clip and one bass clip, and force your other band members to use them instead of their pickups. Ditch the pickup cords; don't let them blend in the pickup signal with the mics. This puts all three of you on the same playing field with regard to gain before feedback. You'll all sound great --
far better than with pickups -- and it will force whoever is running the PA to deal with the situation.
Even if the festival sound engineer isn't good at feedback control, they won't have the lazy option of ramping up the pickup-equipped instruments to full gain before feedback, and then calling your clip-on mic the "problem."
Failing that, then yeah... I guess you need to blend a pickup signal with your mic. Personally, I've gone with "Plan A" above for my mandolin/guitar duo, with DPA 4099's clipped on both instruments. Anyone who sits in with us, like a guest fiddler or bodhran player, gets another clip-on mic. It works just fine whether we're running our own PA or using a house PA, because we're all on the same playing field.
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