Realtime PCR plate cleaning
A possible solution is to use the DNA ZAP solution, which I know many people used in adjacent labs and were happy with for cleaning their DNA free workbench. The product sheet states 


  When 500 ng of template DNA is dried down in a PCR tube, it is rendered unamplifiable upon treatment with DNA ZAP solutions. Additional experiments demonstrate that the DNA is degraded down to free nucleotides.


Please note that I'm not promoting any specific product here and you can purchase any similar product/technology for your particular application. Obviously the best recommendation is to use new plates for each reaction but this/or a similar product can be an option too although the risk of DNA contamination in a PCR based reaction should be carefully balanced against simply using fresh plates considering the product itself is not free either.

The product sheet provides instruction for cleaning/treating PCR tubes hence I assume you use the same protocol for plates if you have the plate centrifuges available in your lab. You can get rid of the solutions by tapping the plates on a tissue to get the liquid out of the wells.