After some quick "research" about this walkers getting-in-the-way assigning problem, I can say that problem is not "global" Lemmings 2 problem. It's just PC and 8-bit (GB, GG, SMS) problem. As I remember, Matt said that he had the source code of the PC Lemmings 2 to help him porting the game to the 8-bit consoles. So, I suppose he used PC version as a model of the game behaving (or it is just a coincidence?). However, there is no problem at all to select digger in the bunch of walkers in any of other 6 versions of the game.

@LemSteven Thank you. It's very nice to see that explanation. But, I think it's too hard for me, so I won't dare to even try this solution. There is also one other (but only possible on the Mega drive) solution for that level:
https://www.youtube.com/watch?v=9rMxSC2nalc
Your solution is much 'cleaner', but looks like very hard to achieve.

@ccexplore I asked you because you said here "emulate DOS Lemmings as closely as possible". I holding back this question for a long time. Why DOS? Is it the first? Is it the best?
I can forgive a lot of things done (or not done in the DOS version). Very annoying is lack of water/lava on the some levels (e.g. Fun 4, 6, 8, 9, 10, etc).
But, number of max 80 lemmings per level in DOS, instead of the 100 in Atari/Amiga version is something that bothers me a lot.

@LemSteven And that's it? You are just declared 100% solution on the level without recorded video, no pictures to show us what to do (and where, and when to do). And you even don't want to bother us with the detailed explanation? Hey man, that's not enough! I want as much details as possible. If you can't record all this on video, I expect some very detailed explanation and schematic pictures.

I must correct myself. I was able to find these installers.
Here they are in the attachments.

I can't find any proof about existence of these installers. However, it is possible to play CDTV and CD32 versions from the hard disk.

Genesis 'Lemmings 2' has passwords, so you can't lose your progress. Just enter the password and you are back in the game. It's not a problem to find all 12 passwords (each tribe has it own passwords) for all completed levels on the internet, but it's a problem to find passwords for all the levels available but not completed. Why is this important, you may ask? Because if you are enter all of the final passwords it's really annoying to play this game anymore. Whatever level you play, the game assume you should be awarded with the final animation and you can't avoid that. As I remember, game even won't to go back to the menu after the animation. So, the only solution is to perform reset.
But, you are lucky because I have all the passwords for the unfinished game with all the levels accessible. Here they are:



My advice is to enter all the passwords (not an easy job, I know) and then save the state from the emulator. So you can start the game, load the state and play any level you want and don't care anymore about saving your progress.

And one more thing, 'Fusion' emulator can work as USA, JAP or EUR.
Can be selected in options menu or with the F-keys:
Options -> Country -> USA(F1), JAP(F2), EUR(F3)
It's easiest to play EUR version, because the game works faster with USA or JAP settings.

I don't know why the 'Beach' tribe is set as a first one to play. Is it accidental or intentional? Isn't it the most logical to start with the 'Classic' tribe (assuming you just finished the original game)?