When talking about cleaning, it is worthy to consider frequency of cleaning being done by rimfire benchrest shooters and NRA smallbore prone competitors. My club has an active rimfire benchrest group as well as smallbore prone shooters. ALL of them clean their rifles religiously after matches and some do during matches. This is after firing 200 rounds or less with prone shooter or 100 rounds or less with benchrest shooters. (note that the dreaded carbon ring will probably not form with this regular cleaning)
These shooters are all highly competitve, all shooting Anschutz rifles with custom barrels or custom actions with custom barrels, all using Eley Tenex or Lapua Midas + ammo.
What this should be telling you is that if you want top level accuracy from a rimfire rifle, keep the barrel clean.
Also note that with every rimfire rifle I have had experience with, it takes from five to as much as 20 rounds to fully foul the barrel for best accuracy after cleaning.
You're on the right track.
Most benchrest shooters clean after every card.