I wouldn't give up on them. I would not bury their stems deep, maybe just above the root ball. Most summer squash takes 45-60 to maturity. I started some in mid July last year and still got a decent crop (I'm in upstate NY.) So you have plenty of time to start from seed.

Summer squash (all squashes) prefer not to have their roots disturbed. You might be better direct seeding them into your garden.

start new seedsdurectly in your garden. They will germinate according to the air and soil temperture on their own terms.It is not a good and practical idea to start CUCURBITA indoors. Once germinated , they an get pretty leggy fast. Even the ones grown by rofessional nurseries in full fledged green houses do get leggy.

I only bought few japanes Cuke seedling from Lowes and they were leggy (about 8") I had hard time to handle and manage them, because I could not burry all those long legs in the ground at once. l planted them in a big hole and put straws around them and packed soil little by little. I seeded the rest of my cukes directly in my garden and they are doing better than store-bought seedling.
So did I with all my squash and gourds. I am harvesting squash now and my gourds have 10 ft long vines. Of course , I am in a warmer zone than you are. But for squash there shouldn't be problem in up state NY.