Again, this is not specific to paw paw, but unless you set them directly in the sun or on a heat source, I doubt a week is long enough to kill them. I'd soak them in a bowl of water for an hour or so to rehydrate them before putting them in cold storage. I would guess that paw paw seeds would have less of a mold issue, so you may be able to get away without the long fiber sphagnum. It is hard to find the live stuff which I like best, but you can get the dried long fiber sphagnum at Home Depot and it works too. The link below shows you which sphagnumto use. The stuff that comes in bales comes from a different place in the bog and is fully dead without the antifungal properties of the long-fiber. Here is a link that might be useful: Long Fiber Sphagnum

Looks good to me. I would keep them wrapped until spring. What is the point in unwrapping them when it is not necessary? If the bud is not good in the spring, bud it again!

Hmmm...well Smivies post got at least one more of my brain cells turned on. Massachusetts does have a fairly broad range of climate (much more so than I would have guessed for such a small state). Some areas, especially in the northern and western parts of the state, stay cold for much longer than I imagined. I should have looked before posting, but was lazy (or enough brain cells weren't firing). Pawpaws have fleshy roots that tend to rot if planted and left dormant for long. That's why you'll always see advise against planting pawpaws in fall or winter (unlike many other types of trees). Even though Smivies seems to have caught my off-timing issue, I'm not sure the instructions on when to plant were stated as meant. If the pawpaws had broken bud at Easter, then you should plant them then; they would have already began their growth. It's if they haven't that you might wait until your May visit. Another way of addressing timing would be to consider where in the state your parents live and plan that way. If they live in the eastern part of the state or around Springfield, plant during your first visit. If they live in one of the colder areas, you might be better off to wait until that second visit. Your goal should be to avoid letting the fleshy roots lie dormant in wet soil for an extended period of time but to also get them in the ground in time for them to become somewhat established before hot weather. See the map linked below. The last frost date isn't what determines root survivability, but it will (in the case of fleshy-rooted plants) give you an idea of when it's too cold for the necessary growth to occur. Here is a link that might be useful: Massachusetts Last-frost-date Map

As long as I stay on top of the watering, they do pretty well--but by being stingy & careless with the irrigation I nearly killed my biggest one last year, and when I went out this morning to take photos I saw that another one has dried out and is really suffering. So, due to my own neglect, I've only got two decent ones left. This one is now my best hope. It's 6 feet high and even made a few flowers this year. This had been the biggest until last summer when the main trunk died due to water stress. At first I thought the missing leaves were due to leafcutter ant, but no such luck. It's now trying to come back from the base, so I'll keep my fingers crossed that it will succeed as a multi-trunked tree (which would make a good base for grafting on a few named varieties). This one has been slow but is hanging in there; it put out a few flowers this year as well. Your request for photos may have saved this one--time will tell. I went out to take pictures and saw it was on its last legs, so I gave it a soak. Hopefully it's not too late. This 10" runt came from the same batch of seeds as the others, and was planted at the same time. Aside from being tiny, it seems healthy enough, so I just leave it alone to do its thing under a white sapote. I include it with the other shots just to make the point that, if you're starting them from seeds (and you have enough to waste some), you might as well plant several in each location and then cull the least vigorous. I kind of got sidetracked by avocados last year, and haven't been paying enough attention to the pawpaws. In Arizona they clearly need frequent, deep irrigation, and one hot day with a water deficit is enough undo several years of progress. They also need deep mulch, which I also haven't gotten around to adding yet. I'll try to do a better job of taking care of them this summer, in hopes of being able to give a better report next year. In the meantime, if you haven't already done so, you might want to join the Pawpaw Fanatics Facebook group: https://www.facebook.com/groups/927257504078942/