Any info or assistance would be greatly appreciated.
My advice, make replacing this thing a priority. This has been a bad idea for a while now, and your time would be better spent on a permanent fix rather then hacking this thing up.
To continue the discussion since it is an interesting problem...
Per the LinuxTV.org Wiki, the Hauppauge WinTV-HVR-1250 has been supported in Linux since kernel 2.6.27, and this version should have PCIe support as well.
(http://linuxtv.org/wiki/index.php/Haupp ... V-HVR-1250
As bthylafh suggested, you could compile a custom kernel, but I would be concerned with having to recompile userland applications due to ABI/API changes. I'm also not sure where you would get LRP source code since it's been defunct since 2003.
You could build a 'like' system with LFS or Gentoo. You would have to reverse engineer everything, and it would essentially be as much work as porting the application to something else that is supported.