Ok ...
I tried the following Glide Wrapper: 
http://www.zeckensack.de/glide/
I installed it, and then I used the default settings for general purposes and for the pre-set stuff for Diablo II, I changed nothing. So, after I installed the Glide Wrapper, I ran the Video Test from the Diablo II directory. Then it detected three rendering methods, instead of the usual two. The third one was new to me, namely "3dfx", so I chose that one, and I tried it.
With that render, the game runs very similarly than with Direct Draw, and it has much better colors ... BUT (yes, another issue) ... the game eventually freezes and I have to press the Windows key, stop the process and reset my default Desktop gamma settings. It just freezes after 5 to 10 minutes of game-play. And I also noticed that there is still slow downs, unusual slow downs, just like in D3D, however they are less common, but still very noticeable when they occur.
At least, in the process of testing, I noticed something strange, and I'll try my best to describe it.
Under the Direct 3D render, when I start-up the game, and when I create a game on-line, I noticed that there is some sort of a "pause" before anything starts loading, with a strange white "rectangle" (very small, and placed vertically) on the top-left corner of the screen, it measures like two or three centimeters, maybe less. It appears before the game-loading process begins. You know when you're in the chat room and you see all the characters on the bottom of the screen that are present in the same channel than you ? Well, from there you can create a game or join one yourself ? Well, let's say I just create a game, then as soon as I press the "Create" button then the screen darkens a little (not completely black, just darker), then that strange white "rectangle" appears, and only then will the game start loading (with the doors opening loading scene).
There, I captured a screen shot of what I mean above, carefully look at the top-left corner, you see like a "missing" part of the picture, well, that's what I mean, it's the "rectangle" I'm talking about: 
http://img95.imageshack.us/img95/7906/76286676iz8.png
I made the rectangle myself in Paint, because FRAPS did not capture the rectangle itself, but that's exactly how it looks right after I click on "Create", except with the rest of the picture a little darker.
Additionally, I can say that the "rectangle" and the "screen darkens" weren't present with my X1800XL under the D3D render.
I don't think I can describe it better. But why do I mention that ? Because I noticed that the rectangle is completely absent under the Direct Draw and 3dfx renders ! It's just not there at all. Also, under those mentioned renders, the screen does not darken before a game loads up, everything goes smooth and fast, just like it did with my X1800XL under Direct 3D. So I believe there is must be something wrong concerning the Direct 3D render. But the slow downs are also present under the two other renders, just a little less...
I don't know what to think anymore ...
I made 100% certain that all my other games and my synthetic benchmarks ran correctly, and they do ! All my games are super smooth, my GPU is providing me some performance that my X1800XL could never even dream of, so it certainly ain't the GPU itself. I also made sure that I am running the latest DirectX update, and I do, and to make sure of it I just re-installed it (latest one from Microsoft.com).
I ... I just don't get it. I can't get it, all of that is way beyond my comprehension capacities.
EDIT: I don't know if I mentioned this though, 
but I tried in Windowed Mode, 
under the Direct 3D render, and 
it plays super smooth, 
and it never slows down at all, just like it was with my X1800XL, there is no "rectangle", no darkening screen before the game loads, nothing like that, just pure speedness of execution and game-play bliss all over the place. But that's in Windowed Mode ... which is way too small, and it forces on the eyes after a while, I can't play like that, and things are so small that I can barely see my enemies especially in already dark areas like Durance of Hate in Act III.
So if it plays with unreal speeds under Windowed Mode, 
in D3D, and that it shows absolutely no problems at all, then it cannot be a drivers problem, can it ?