Okay this digger picture actually show you dig 2 pixel behind than lemmix.
If that's what it looks like for you, I wonder if maybe you are not looking at the correct level or replay in Lemmix. You need to be looking at the 0304.lvl level, which amongst other things has an animated waving flag object added to the right of the level (to help distinguish from the original), and you also need to use the replay whose filename has "SNESTest" in it, instead of the original one I posted for the 13-skill DOS record. You must use F4 in the main menu to go to the settings menu that allows you to toggle "look for LVL files", in order to make Lemmix load the level from that file instead of using the original official version from DOS.
If you don't see the added waving flag object in the level, then you are using the wrong level to play back the replay with. I wouldn't expect the solution to play out correctly in that case though, so I don't know what to say. Did you actually verify that the replay successfully saved everyone? You can press Spacebar key a few times in Lemmix to skip forward to the end and see how many % saved. If it doesn't say 100%, then your setup in Lemmix is incorrect.
Make sure you performed the two release rate changes: from 50 to 54 after 8th lemming comes out, and from 54 to 56 after 32nd lemming comes out (which is also around the time you assign builder to 30th lemming).
If you end up with 1 lemming stuck into metal, that means lemming arrived too soon. If that lemming is the 34th lemming out, maybe you can try and see what happens if you skip the 54->56 release rate change, which would put him 1 step behind.
Hope you can fix the problem with video recording soon.