A hack to simply make it play normal music on these levels would be sufficient.
That would be much easier. Actually, if we based it on ONML (which has no special graphics music), it would be equivalent to hacking it to support more than 100 levels, which I think should be relatively easy.
However, one thing I do want to ask you, since you're the expert on mechanics: If you know the trick I'm talking about, do you know if it's possible to make the Oblivion trick work in DOS/Lemmix?
I think I've come up with a setup that will work. Unfortunately, the only graphics set I've found suitable for creating it is the Pink Style. And actually, even without worrying about the mechanics, the Brick style in DOS ONML turns out to lack the vertical version of the staircase that your Cheapo level uses, so it wouldn't have been possible anyway I think to even replicate just the graphics. Another possibility is to make this a special graphics level--create the non-staircase terrain in LemEdit/Lemmix, take a screenshot, and then edit the screenshot in Paint to put in the staircases. I can then use various programs to turn the screenshot into a VGASPEC.
Attached are two test levels. OBL1.lvl illustrates the general setup, but it is fairly inefficient in terms of terrain usage: each staircase takes 15 terrain pieces. Because blockers cannot overlap in DOS Lemmings, the total amount of horizontal space taken up by the 18 blockers would require 28-30 staircases to cover, which exceeds the limit of 399 terrain pieces in DOS Lemmings. OBL2.lvl is a second setup that is more efficient in terms of terrain piece usage. The test level uses up 308 terrain pieces, leaving you with 91 to construct the rest of the level, which hopefully should be more than enough.
Great care must be taken in how the staircases are positioned. Note that in both test levels, the leftmost staircase, its upper-leftmost pixel is at (300, 60). Notice that both coordinates are multiples of 4. You may move the terrain around, but you must take care to keep the position of that pixel at multiples of 4 for both x and y, and you should keep the spacing/relative positioning of everything else (all the other staircases, plus the ground level)
exactly as given.
Because of the huge number of terrain pieces involved, if you're not going the VGASPEC route, it is highly recommended that you use Lemmix to create/edit this level, since Lemmix gives you the means to move the entire terrain setup as one unit rather than 308 separate terrain pieces.
Based on my understanding of the game mechanics, the setup should work as desired. A blocker standing on a terrain pixel whose y is a multiple of 4, his "blocker field" will only extend downward to 4 pixels (including the one he' standing on). So the step height of 4 pixels is just enough to cause the lemming below the step to not be affected by the blocker. The horizontal multiple-of-4 alignment ensures that the various boundaries of the blocker field all line up with the steps to achieve the desired effect. Anyway, if you do find some serious problems with the given setup, let me know and I'll try to find a way around it. (This is where Lemmix again can be helpful, since you can just provide a replay to illustrate the problem instead of having to explain it in words.)