After much sound, fury, hair pulling, and bad language, the results are in.
Programs that recognize the W7 app data path variable, keep their data outside the program file tree, and work when installed to the default directory (Program Files (x86)):
FLdigi (Note 1)
JVComm32
TrueTTY
Programs that should probably be installed in a different folder you create yourself (I called mine "Radio"):
DSCdecoder (Note 2)
MultiPSK (3)
PC-ALE (4)
PC-HFDL (5)
POSFIX
Spectran
1) Created files under "Users," not in program folder.
2) ITU lookup won't work installed under Program Files (x86).
3) Some confusion over whether or not to run INSTAL.exe after unzipping.
4) Do not leave "create desktop icon" checked. Create shortcut manually in program's home directory, and drag to desktop. In fact, do this for all these programs.
5) Go into ground station file, change "AUCKLAND - NEW ZEALAND" to "AUCKLAND - NZ" due to a bug unrelated to platform.
As always, your results will be different. That's what worked here.