While I don't know exactly what you've got there, my suggestion would be to treat these vegetables as you would any other tropical - eggplant, pepper, tomato.

Start the eggplant indoors 6-8 weeks before your expected last frost date. The "pumpkin" can probably be started indoors 4 weeks before your last frost date. Then harden off & plant out like everything else.

With your shorter growing season you may want to lay in a supply of row covers to help extend your harvest.