You can pick out separate seedlings carefully, transplant them into successively bigger plastic cups & then into actual containers with intent to stall until can work the ground.
Watch out for over watering & be consistent in the planting mix you use. ((See G.W.'s hydroponics & container forums for growing medium you can adapt in the interim.)
As for pumpkins & all the ground vine crops: seeds tend to jump up robustly & they really do not like their roots disturbed once they are big.

Any chance you could convert a portable cold frame into a hot frame -- dig a 6-inch trench in the garden or raised bed, layer in 6 inches of fresh or near fresh horse or cow manure -- cover with an inch of sand, place the frame over the bed -- you now have hot frame that will be 20F warmer than the outside temp. You can grow on your seedlings in pots until transplant out time. It's an old Paris-market garden trick.

Here is a link that might be useful: HarvestToTable.com