I'd guess the problem is not enough tension in FD cable. Try unscrewing the barrel adjuster at the cable stop a bit to see if you can hit the mid on the way up.

Can you take good pics of mid ring teeth profiles? One can usually visually verify worn rings.

As to replacement rings, Universal carries Dimension 110mm 36t mid rings, but $54, ouch. Could probably find a like new 105 triple crankset on eBay for that.

Couple of other notes about things mentioned:

36T small rings are common on CX cranks.


Doubles are actually fairly common on MTBs these days. XTR, XT and plain ol' Deore doubles are available.