222 is S2 solenoid, open circuit.

Well, the S1 and S2 solenoids are attached to the valve body inside the frontward mounted trans pan (cover). To remove that cover, the engine must be supported while the front of the subframe is lowered for access. In a shop, on a lift, it's not a difficult job.

Being that there's a definate fault code for what should now be obvious, I'd have that soleniod (plus the S1 too while they're there) both replaced and see if that fixes it. I'd be far cheaper to do that than replace the trans but sure, it's also possible that the trans could have more serious internal problems as well so it's somewhat of a gamble (maybe?).