So, to summarize, hooking your cable TV cable to either Tivo causes it's output to mess up for both previously recoded shows and newly recoded shows. With no cable TV cable attached, the outputs are fine for older shows. ROKU has no problems.
It's a grounding problem between your cable TV cable entry point, Tivos in the closet and your TVs. The ROKU doesn't exhibit the problem because it doesn't involve your RF cable.
Putting a long distance between your Tivos are TVs can be an issue itself but let's put that aside for now. You didn't mention if you also connected cable TV directly to your TVs because that could complicate things further.
Try the following experiments:
1) For your S2 and it's TV, use an extension cord and connect the TV's AC input to the SAME AC outlet as the S2 Tivo supplying video signals. Unplug all video cables from the Tivo HD and other set to get it out of the equation. Ideally, you could move the TV next to the S2 and use the same AC outlet and short video cables. See if this helps.
2) Repeat 1) but with the Tivo HD and it's TV. Remember to unplug all video cables from the S2 to get it out of the equation.
In both cases, check with and without attaching your cable TV cable to your Tivo. I suspect that your picture will be OK, maybe not perfect, but better.
If indeed this fixes the problem with the longer S-video and component cables stiil in use, you can get an RF isolation transformer to connect right before your Tivos. Something like the Calrod isolation transformer at the bottom of this page
or similar. An isolation transformer breaks the grounding between the CATV system and your home.
If the test with the AC extension cord doesn't fix the problem, then definitely move the TV next to the Tivo and connect AC and video cables directly (no long cables). This should mimic the case before you did your equipment re-shuffling. Make sure you're OK in that setup. If it's clean, then use your longer 25' cables and see if that's the grounding culprit. I've got suggestions on that front but let's not go down that route until a AC grounding is completely ruled out.
Other things to check are 1) Make sure your CATV is grounded at the entry to your home. Your CATV provider should have a ground wire between their entry point and a cold water pipe or other earth ground. 2) House wiring. The Tivos and TVs could be on separate circuits in your house and those could have a grounding problem.
See how far this gets you and comment on any findings.