First tho't is that you only have to worry about your problem if you are shooting at ground squirrels beyond 200 yds. (That's supposed to be funny
However that problem would drive me nuts:mad:
Here's what I'd try.
There should be no need to clean the rifle prior to shooting 15 to 20 rounds (unless your experience with that rifle indicated more frequent cleaning is appropriate)
You mentioned "slightly fouled" bore. If that means 3 shots and not partially cleaned, fire say 5 in a session to foul the barrel then don't clean. When you come back or when you have duplicated the environment from storage to the range, see what that first shot does.
If It's in the group the rifle likes more fouling.
Second thing as suggested above is let it set at the range, in the shade, for at least 30 minutes before shooting.
If it isn't in the group I wouldn't do any thing to the rifle until after this season. You're only off 0.5" on the first shot which is 5" @ 1000yds which isn't noticeable in the wind and mirage especially in Idaho.;)