You can get DSP-based feedback eliminators that work well and are not
outrageously expensive. We use a Behringer DSP110 Shark unit, which
you can get for well under $100, and it works well for us. Google
"feedback eliminator" and you'll get lots of hits. I wouldn't even
think about trying to build one on my own, with such units available.
I'm sure there are better ones for more money, and others at similar
cost that you should also consider, but I don't personally have
experience with them.

Cheers,
Tom