yeah, i don't really find a reason why call would be > than jam OTT.
as played i guess we have to close our eyes and call river, once in a bluemoon he is vbetting worse like AJ/A9o and sometimes just random spazzing.

yeah go slightly bigger turn and shove over his raise

We can be really happy in this strange spot that he has just a 40% bet left at the river so I would call pretty confidently. Also we might be beat most of the time I cannot see how we win so rarely that a fold is the better choice (we need to be good 22%)

Also TT is the hand making most sense his stats are fishy enough that we could see some strange things here. On the other hand if he was a strong reg he might find some bluff-checkraises on the turn after the flop checks through leaving him with a cheap all-in river bluff so I would call then too.

Probably the only opponent type against whom I might find a fold is a recreational who plays decently enough to have reasonable preflop ranges but would then never get the idea of bluffing the turn. But with the tiny bet I'm not even sure here.

What are the benefits of shoving the turn over calling given we call his river shove:
+ shove: He will call all his weaker flushdraws because of the pot odds he might sometimes not put any more money in on the river.

Possible merits of call: Him checking a weaker two pair or AK to us but I'm not really thinking he ever would with 40% left? Also trapping doesn't seem so attractive for him here with so few left? So shove should work good here.