Don’t count on T.38. I’ve seen docs that say that you have to start with a normal line and then renegotiate. I’ve used a couple of the Grandstream HTxxx ATA devices myself, though I prefer the small Patton boxes. I have some fax systems that even use VPN tunnels using a G.711 codec and nothing else. Grandstream has a couple of options that allow to fine tune these things.
The problem with your kind of problem is that someone has to enable a couple of log options and then change a couple of things based on what gets printed. At the end of the day, $400 may not be that much if an engineer spends a day on that. On the other hand your setup looks a bit weird and overly complicated. I’d probably not use the POTS device but go straight into FreePBX and maybe then I’d use a simple ATA device to hookup an old-fashioned fax machine.