I would be looking at the frequency of cleaning in addition to testing after cleaning. What your current process is saying is that your cleaning is effective if it passes after a retest, however when did the issue start to proliferate? You should be looking at root cause of the issue to prevent reoccurrence which would most likely be cleaning the screen at an increased frequency or at minimum swapping it out.
Throwing 3 swabs for a retest after cleaning would depend on how large the screen is. I generally composite swab so I can review a large area with one swab. If I get a positive then I break it out into specific areas to understand where the failure is coming from (seek and destroy/vectoring). Doing repeat test, cleaning, test, cleaning, etc. is more of a cleaning validation IMO.