As the experts above have mentioned.....
The RD-MT62 was part of the Deore II group from ~1989 to ~1991. It was the replacement for the Deore XT group?
It's rated at a 38T wrap with 32T max cog. Specs set by lawyers!
Heck I can get 32T with a 1st gen 105 RD (not that much chain wrap though).
This is either a 30T or 32T cog.
The pulley cage on the RD-MT62 can probably wrap up 6" of chain. You may have to add a link or two but it should easily cover a 34T FW cog with a very small chainring. Trial and error.
On triples I usually only run the largest 3 or 4 cogs with the smallest chainring. Eliminates possible chain rub on the middle ring.
I prefer steel pulley cages on my long arm RDs. Crisper shifting, plus they're stronger and less likely to get damaged. The few grams more than alloy arms is worth the security.
Deore LX, it's only running on a 28T cog but the small chainring is a 28T.
Later model Deore LX running the same 28T x 28T combo.
First generation steel cage Huret DuoPar Acier RD from 1975-76 (not an Eco), 13-32T FW, 30-46-50T CRs.
Except for 2 or 3 of my bikes I can at least shift into and out of all the gear combos without any problem. I'm not currently running any 34T FWs, they're a lot of "iron" to drag around. A 30T or 32T with a 28T to 30T CR is usually enough.
If I need anything lower, I shift to my "W" gear... I get off and walk - need to preserve my olde knees!
verktyg
Chas.