I have implemented climbers and floaters now. So now pretty much all the original Lemmings skills are there, but with some twists. E.g. the climber can hang on to a perfectly horizontal ceiling and "walk on the ceiling" that way - it falls down when there is even just a tiny bump, but you could e.g. design a level with a "rope" which climbers can use to hang on to. The floaters are like in the original (parachute opens when they are falling too far), but they start gliding in random directions (if you do nothing) or in a direction you control with the dpad.
The core of the game is now more or less working (this was the fun part for me), but there's still a lot of more boring implementation work to be done, like limiting the number of skills, a game over screen (for winning and losing), a level select menu, etc. More fun will be to add music and sound - suggestions are welcome.
It is now getting close to ready to release an early alpha version that level designers can use to test their own levels. I expect that to be ready before christmas.