I've attached a picture I took and did some work on to show how to perform this leech. I haven't messed around with this in MAME with frame advance yet, so my method is still just an estimate.
1) Jumpman needs to have his front toe line up with give or take 1 pixel from the green line.
2) You need to jump as soon as the front of a rolling barrel reaches the yellow line.
3) You need to Jump as soon as you can after landing. Any running in-between jumps lowers the likelihood of pulling off the leech.
I use the little triangles within the girders to help with precision.
NOTE: In the picture, neither condition 1 or two has been met. Jumpman needs to move over a bit more as he waits; the barrel has more distance yet to travel.