Update: to my surprise, I was able to locate the backup that has all my stuff from the old laptop.
There were no notes, but the source code and compiled EXEs for the tools I created do exist in the backup, and it looks like I also already had a copy of the data for Mac Holiday Lemmings 93 as well.
Unfortunately, while those pre-existing tools seem to work as-is on the data from Holiday Lemmings 93, the extracted graphics ended up all blank, or in some cases encountered errors during extraction.
So it would seem that something has changed slightly or a lot format-wise between Lemmings and Holiday Lemmings on the Mac. It is not clear at the moment whether I can get past this problem. If it's a totally different format then most likely not. If it's just slightly different, then maybe, but it will still take time to work out and the holidays are over, so I can't promise spending much time on this in the near future.
namida's alternative idea of creating a custom level with all pieces could be viable if the level file format is basically the same as DOS Lemmings, but you will need to first find on the web a resource editor for Mac files that runs on the Mac, in order to change the levels that come with the game.