I managed it with +1 climber, thanks to a trick that I don't think has been mentioned in the glitches/tricks threads (and tbh I don't know which one it belongs in).
I think it has to be considered a glitch, because the reason it works is basically the same reason for the miner glitch. The expected effective coordinates for the movements during one mining stroke should logically be
from (x,y) to (x+2,y+1) and to (x+4,y+2) [R]
[+y goes down, x doesn't matter which direction is +]
but with the glitch, it is actually
(x,y+1) -> (x+2,y+2) -> (x+4,y+2) [W]
In particular, the other miner quirk about being able to skip one-pixel-wide gaps do not apply here, since trigger areas in PC Lemmings always have a minimize size of 4x4. If the miner's positioning were to behave logically like in [R], then I don't think the trick would've been possible.