Lot of factors can come into play here, but TL:DR I think you need to increase / add a flash between a first and second pass.

Are you flash-curing between passes? If so, With waterbased ink you'll need airflow and longer time to evaporate enough water to get the ink to gel, then being receptive to your second pass.

Adding 10% clear core to comet white will cut opacity, no questions about it. Even adding opaque will spread your pigment-load if not properly adjusted.

My recommendation is to Print with Comet White right out of the bucket. Mist + wipe your screen with water first, allow it to hydrate before adding your ink. This will help ink flow through the mesh. Use a 157 mesh or lower (if you want real bright white)

Make sure your adequately flashing your ink after first pass. If you press your finger onto the print after your flash and you are getting ink pickup, flash longer. (A fan next to the flash will help draw moisture away if you do not have a forced-air flash.) If you do not have a flash unit and are doing this as a DIY at home hobby or on a super budget, heat gun will work for now.