I managed to find the 56 on every exit first, before returning to the first exit I'd tried and realizing I'd made a rookie mistake...that's about an ideal an experience as one could hope for :)
Great level set.
For this one in particular I just randomly pressed buttons on autopilot until I somehow solved it after about 15 attempts. I don't understand it any better now...
So far I've got a four-off path which is pretty neat. Hopefully I'll be able to get it soon.
15 years later: not soon, but I got it in the end. :) Good cuts to get the 4 off!