Dictionary says that pumpkin came from French pompon (large melon) and was originally pumpion. English colonists named the orange melon they discovered in New World pumpkin.

Maybe it was joke pronunciation, calling large melon small. It could be a term of endearment for favorite melon. It could be they wanted to distinguish between all large melons and this large melon. Or it could be pronunciation drifting from use.

... or were early New World squash just of the smaller variety and only recently have we selectively bred them once that Mendel fellow started messing around with his peas?

I don't think pumpkin gets is name from the "-kin" diminutive.

Etymologyonline says: 1640s, "gourd-like fruit, of a deep orange-yellow color when ripe, of a coarse decumbent vine native to North America," an alteration of pompone, pumpion "melon, pumpkin" (1540s), from French pompon, from Latin peponem (nominative pepo) "melon," from Greek pepon "melon."

So the "n" has been on the end of the word for a long time.

OED says it was remodeled with the diminutive:

> Alteration of pumpion, variant of pompion n., with remodelling of the ending after words in ‑kin suffix.

Jack o' lanterns are large, but plenty of the older varieties are softball sized.