Steve, to clarify, do they conduct when connected in reverse, even when "coil" is de-energized, or are they open when connected in reverse, even when "coil" is energized?
If the SSR uses a P-channel MOSFET then there's an inherent diode from drain (anode) to source. That means if you reverse the polarity to the SSR, current will flow through the body diode. It won't take much current before the device burns up.
You should be able to test if there's just a diode between the load and power terminals. Connect multimeter, (setting to ohm/diode) with positive lead on load terminal and neg lead on power terminal. You'll get a 0.7V reading if a diode is present.
I think searching for a 200A SSR is asking too much. There are more efficient ways to disconnect a 150A load (inverter). I'm pursuing a low current SSR. My loads consist of a 2500W inverter and other loads which are less than 8A. A 20A SSR is more than adequate. I got some mosfets on order and will see about putting together a switch. Reference my previous post.