can you fire it up once a week? that would prevent any fuel problems.
DO NOT DO THIS!
While it MAY prevent carb/fuel issues it will (unless you run for at least 20 mins, get it properly up to temperature, and run it through all gears with the clutch out) :-
- Create condensation in the oil, leading to emulsification and rust on non coated parts
- Create condensation in the exhaust, leading to rusting from the inside
- reduce charge in the battery (although the optimate as suggested, will alleviate this one)
- foul the plugs
As MaddogMcQ said, brim the tank up (so no rust can develop), weight off tyres (unless you're prepared to sacrifice them, sounds as though you are), and either an optimiser, or take the battery off the bike and keep warm (ideally not in the house though, in case it leaks fluids (which you'll see) or fumes (which you won't)). And do not be tempted to start it to "turn it over".
Me, I wouldn't worry about the mice issue, but sounds as though thats well covered
That's what I've done for the last 14 winters with my 1998 FZS600, and it's always fired on the button come spring. There is not a hint of rust in the tank, and its still on the original downpipes (yeah, those ones that are allegedly made of cheese) despite being ridden on salted roads a number of times.