We have been full-timing and Workamping for nearly 14 years, most jobs have been at least 3 months (this will be our 4th year at Campbellsville). we had the same concerns as you about long term sitting when we started. Bottom line: 3 months is not really considered "long term storage" per several tire companies.
Use of plastic "leveling blocks" is good to prevent the tires sitting in the water when it rains (better than wood, but wood is ok, just heavier). Cover the tires to minimize UV damage. And relax, have a glass of wine.
What park will you be at? We will be at Three Springs Resort in a silver cousin ('86 Avion). Nice big sites, QUIET!, No one bugging you to come join this activity after a long day of work, and the owners are nice.
FWIW: we have always had dogs, and the mice have visited us in the past. They didn't mind the dog
They quit coming around 'cause we left some "special food" out for them on their runs. Gee, didn't mean to offend them.