I am no Model 340 expert, I am only going off of memory here............

IIRC the 340 has a different sized barrel nut and so the wrench for the 110 won't fit it. Also IIRC the thread pitch and diameter is different on the 340 vs the 110 series.

Might check it out.

You should be able to have a barrel made, but I would check out the above and proceed with those questions answered. FWIW I have had the chance to fire a very pristine Model 340 with a low low round count in 222 Rem. She was a shooter, and if I found one that needed a re-barrel I would definitely pursue a new barrel if it is possible.