Ron...
If you have a collection of the relevant links you've found at archive.org, and if they seem to be stored in a common location there (or if there's at least some recognizable pattern to the locations of the stored archives), perhaps some fishing with a program like HTTrack Website Copier or one of the Teleport products might help to gather them up for you and allow you to "import" or mirror them on the new server.
Worth a shot? Maybe??
If you're not familiar with the programs:
http://www.httrack.com (free)
http://www.tenmax.com/ (requires license purchase)
I honestly don't think you've got anything to lose by at least trying the HTTrack, since it's free,
if the file locations at archive.org have enough of a structure or recognizable pattern to make it feasible (i.e. "target-able")... Who knows what it might be able to retrieve (and HELP organize)? And, if the process itself shows promise, perhaps the more sophisticated Teleport products might be able to handle anything that HTTrack misses.
Good luck if you decide to try it...