I've also looked into writing a display driver for Windows 9x, and I could be wrong, but I doubt there's any WDM support for it at all, even in 98SE and ME (please correct me if I'm mistaken).
For the curious, here's an overview on how display drivers work on 9x. Graphics drivers for 9x are basically the same model as they were in Windows 3.1. That is, a 16-bit (yes, still 16-bit even in Windows ME) DLL (commonly with a .drv filename) which initializes hardware and implements every single GDI drawing function. A few things changed in Windows 95. The first is that drivers no longer have to implement all of GDI themselves (a huge pain in the arse for anyone writing Windows 3.1 graphics drivers) and can just call a Windows provided library called DIBENG to do so. The second is the introduction of Plug and Play, which requires writing a VxD to interact with it. Since VxDs are ring-0 32-bit code, it was common practice to put a lot of the hardware functionality into the VxD and have the 16-bit driver call the VxD to perform tasks, since 32-bit code performs better.
I'm not entirely sure how Direct3D and OpenGL fit into this picture, as I've never gotten to that point. I know OpenGL uses Installable Client Drivers (ICDs) which are DLLs that replace the functionality of the Windows-provided opengl32.dll. Those ICDs likely call into the VxD to interact with the hardware and provide acceleration.
Short of Intel releasing the source code to their old Windows drivers (We all know that ain't happening. Only their Linux drivers are open-source), there's not much we can do. The only viable option I see is to leverage something like Gallium3D and Mesa to provide hardware acceleration. Gallium3D is supposed to be an OS-independent framework for graphics drivers, but it's quite complex and really geared towards systems like Linux and the BSDs, and it would be a massive amount of effort to port that to Windows 9x. However, if OpenGL is supported, Direct3D shouldn't be too difficult as WineD3D can implement Direct3D on top of OpenGL.