It seems that I may have given up too quickly on the next-gen ground poly after all. A few days ago I responded to a thread over at the Lockheed website regarding the removal of support for FS2002 ground polys as of P3D v3, and one of the devs for P3D replied with a bit of information on the new system they created for creating ground polys moving forward. By sheer chance I happened to see it, and it turns out there was only one reason why I couldn't get it to work: I had z-write turned on (apparently you need to turn that off in order for the z-bias to take priority). So, I went back and tried again, and I'm excited to announce that it's now working flawlessly!
Everything nice 'n' shiny. Not final, of course. I got rid of all my specular textures after I scrapped the idea last time around, so I just enabled the basic specular properties for all the materials to make sure it was indeed working.
To make certain everything was totally flat, and not offset like I failed to notice the first time I tried this, I carefully examined the shadows to make sure there was just one, completely flush shadow on the ground. I'd like to point out, this shot was taken with shadows enabled for objects with no-shadow tags. Because there are still no shadows visible from the ground markings (even after examining from various angles for several minutes to make sure I didn't miss anything), this is a strong indication that the polys are indeed flush to the pavement.
Final shot. I flew around for a while high above the airport to look for any signs of z-fighting, and after twenty minutes I had not encountered any. Here's a picture from just south of 31. You'll notice that everything appears properly layered, and there is no longer any texture bleeding/blurring.
------------------------------------------------------------------------------------------------------------------------------
So, to sum it up: the verdict is in. After a week of uncertainty, I've decided to stick with the P3D ground after all. Now, I want to reiterate, this does not work in FSX. The z-bias variable was only added in to the SDK with the most recent release, and as such, FSX does not contain the code needed to utilize it, so attempting to use the new ground poly in FSX results in extreme z-fighting. In the interest of maintaining compatibility, I'm developing this in tandem with the FS2002 ground for people still using FSX, but people who use P3D will be able to use this with all the new effects after all.