Pixelation and sound issues are usually the result of a loose coax connection, damaged cables, or a weak signal caused by too many splitters/long coax runs/etc. I don't remember the screen or the fields offhand for TiVo diagnostics but the dedicated CableCARD group should be able to help you determine whether the TiVo is getting the proper signal.
For your TIVO, channel to number assignments are handled by TIVO/Rovi and not Spectrum. You may try TIVO support. Good luck with that.
Quality issues are, of course, Spectrum issues that may take a while to sort out after a round of channel assignments changes. Cold booting your TIVA may help.
There were channel changes in May and this information was not updated to TIVO units. i watch PBS on Channel 6 a lot but Spectrum changed it to channel 2. So I have to look at what is showing on Channel 6 and set up a manual taping on Channel 2. Very confusing when I am looking at the taped shows.
Also, quality on PBS channels is now horrible. Pixelates all the time and sound cuts in and out.