I think cf is best. I'd probably jam AsA. It's a pretty awful situation for us if we are always checking to c/f river. I don't think anyone would pick up on it at nl10 but if they did we would need to bet bet check some flushes as well.

This is one of the worst runouts so I would x/f this river.

never betting river, likely folding most riverbets ( it depends ..:) )

As played, x/fold river is best I think.
But I would consider x/calling turn. You`re in a really bad spot if you get raised on turn, and he will pick up the betting probably with a strong Jx, AsX, other semi-bluffs on turn anyway...

I don't think you`ll get 3str of value often enough on such a run out to go bet bet bet, so if you are going to give up a street of value, I don't know why woudn't it be the turn and keep is range wider.

My thought process might be wrong here, fell free to criticize.