Notes on the installation process:
1) I had to install the 4870 in slot 2, though since that slot is 16x, as well, I doubt that will make any difference.  In the case of this 2gb Vapor-X card, the screws on the back of the card are not what interferes; it is the heatsink.  The 4870 works fine under Windows 7 RC, which is what I have on my boot camp disk.
2) I followed the custom ROM creation instructions, and they worked perfectly.  The 24" Dell LCD that I have attached to the 4870 lights up on power-on, and I can choose a boot target.  However, when the OS loads video drivers, the screen goes dark.  I looked in System Profiler, and the card is detected as a 4870, but has no displays connected.
OK, no luck with any of the cables that I have on hand.  I have tried straight HDMI, straight VGA, and VGA, with a VGA-DVI adapter, based on issues I had read about earlier.  It looks like the sole DVI port on this card is not activated by the OS X driver.
I have also downloaded and installed Netkas' universal injector, from 
http://netkas.org/?p=104, to no avail.  I also tried Netkas' Natit for ATI, from 
https://forums.macrumors.com/posts/7643911/.
Any suggestions?  I'm assuming that VGA BIOS hacking is probably going to be required, to make this card work.
Thanks!