Seems like you didn't get any answers, perhaps because 3 channel seems too home theater for this crowd? Anyhow, for inexpensive, high quality class D amps, I'd recommend VTV, which uses popular Class D modules to build inexpensive amps in whatever configuration you like. I had good luck with a basic 2 channel amp from them. Looks like they can easily do 3 channel, as well. Using Hypex nCore modules, it looks like you can get one for under $1k. See here:
https://vtvamplifier.com/product/vtv-amplifier-hypex-nc252mpnc250mp-three-channel-amplifier-3x250-w/