Looking at the REV01 version of Sonic 1, I can see why it's Rev01. They pretty much completely overhauled the entire BG deformation part of the engine. The drawing system has been changed (and from what I've seen, more similar to the way Sonic 2 does things) and the deformation data for every level has been changed to fit this new code. Also, in every level besides SBZ2, it was used to enhance the deformation effects. To see the difference in your own Sonic 1 rom, you'll have to do the following:
1. Download every text file below. They contain all the ASM you need to perform this conversion. note that if you edited code in any of the code you're about to replace, you're probably not gonna get those edits back without substantial recoding, so be wary.
2. First, we'll do the easiest change. Go to label Obj0A_WobbleData in hivebrain's 2005 disassembly and replace the entire block with what's in lzwobble.txt. The programmer's extended this array so it would also be usable by the deformation data even though it was designed to be used by the water bubbles.
3. Next, we'll do the BGScroll data. Go to BGScroll_GHZ in the disassembly. Replace everything from there until the end of BGScroll_End with whatever is in bgscroll.txt. The starting deformation data for every stage needed to be changed. To be precise, it prevents bugs that occur in the scrolling in SBZ and SYZ, and prevents a bug that causes GHZ's bg not to appear at all.
4. Next, we'll do the deformation data itself. Go to Deform_GHZ, and replace everything from there until the end of Deform_SBZ, straight down (right before ScrollHoriz) with the contents of bgdeform.txt
5. The new Bg drawing system required a different method of scrolling the BGs themselves. Go to ScrollBlock1 and replace everything from there until the end of ScrollBlock4 with the contents of blockscroll.txt. Don't worry that there are six BGScroll functions now, that's taken cared of.
6. Finally, the biggest part: the BG drawing code. Go to sub_6886 and replace everything from there until the end of LoadTilesFromStart2 (that's a VERY long way, up until MainLoadBlockLoad) with the contents of bgdraw.txt. This should also result in a duplicate label loc_6ED0 in the resize_GHZ3boss routine. Just replace both instances of that label in that area with whatever you like, and you should be good to go.
7. Assuming you haven't changed the backgrounds of your levels, compile it and give it a go!
I'd just like to credit Hivebrain for attempting this first, and Tweaker for his assistance when I had some issues to resolve. Tell me if I forgot anything, and put any questions or comments here.