The indications are that the extra ventilation of a SBB seems to invigorate the bees. I designed mine with trays. When I finish making them, I plan to use with open bottom during the spring and summer as this has the added advantage that the mites are not going to climb back into the hive.
The tray is there, if needed, so that mite contol can continue all winter long. Greasing the tray just like you would with SHB prevention gives you one treatment for two problems. In winter I believe it will be possible, on milder days, to check, wipe clean, and re-grease the trays about once every 3-4 weeks.
That's my action plan--I't one I've decided on after a lot of consideraton.