Hi,
I have just been putting the seeds between moist paper towels and then transferring them to small pots. They are germinating fine and just starting to come up in the pots, so far I have about 10 started and more waiting to germinate in the moist towels. So far so good but I am starting a bunch in case some don't make it. I have the seeds in the fridge and I would think they should be be fine in June. I can throw in some extra seeds if you're worried that some won't germinate but I think they should be okay since they are refrigerated.
Frank