Do you get those good SNR and RS Correction numbers on a channel while it is locked up or pixellating badly? If the RS numbers are always zero or small, I doubt if excessive signal is your problem, although notice this statement from a TiVo support web page:
NOTE: If your signal strength is at 100 and the video looks fine - this is not an error. The signal strength meter sets 100 at a safe threshold. If the signal is at this threshold or a bit beyond, your picture quality should be excellent. If the signal strength is well beyond the threshold, it will still register as "100", but you may experience poor picture quality as some box components cycle in and out of "protect" mode to prevent damage.
The web page is this one:
Attenuators are cheap, e.g.:
Get one each of 3, 6 and 10 dB. Just unplug the coax from the TiVo, connect the attenuator then connect the cable to the attenuator.
I also suspect a power supply problem just from your description of the symptoms. Recommend you measure at least the 5V (+/-5%) and 12V (+/-10%) under load. And look for bulging caps:
, look at post #2.