Does the birdhouse's inverter have Arc fault protection as well?
I don't think so. When I looked at the ProSine for our RV (I bought an AIMS instead because it's 50% bigger) they had two different ones I could get. One had a built-in GFCI plug on it and it was designed for marine/RV with a floating neutral. The other model had a hard wire with a transfer relay in it, and it had a bonded neutral. I don't recall ever seeing anything in the specs about arc fault protection in them.
The ProSine inverters are highly regarded in the RV business - a lot of new RV's come with them factory installed now.
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Chris