Hmmm. I've been running tvheadend for about two years on a variety of TBS, Hauppauge and PCTV adapters, DVB-T/T2/S2. I've never had this.
If your muxes are changing, I can only assume that you have "autodetect muxes" on and - for whatever reason - tvheadend is deciding that you have new muxes and trying to tune them in. I'm not enough of a satellite expert, so I'm thinking in terrestrial terms, but I wonder if you're picking up confused signals due to a slight misalignment or other 'leak' from some other signal source.
It's possibly diseq support - I don't use it - is it practical to wire up directly to the LNB and see if the problem goes away?
The only way to eliminate your driver/fw is to try a different distro (e.g. Ununtu live) or OS (e.g. Windows)... the latter obviously forces you onto a different backend as well (e.g. NPVR, Argus, WMC) so doesn't immediately prove anything even if it resolves the issue.
Is there any pattern to the changed muxes? Are they from the other satellite, or can you trace them to anything else that might be broadcasting?