If you have a warm sunny place to bring them into for the winter, it should be a breeze. This works well for me here in Northern NM, where I would normally have them inside by early October and back outside in May. Unfortunately I have not had fruit because of the pollination problem. Supposedly strawberry papaya plants are either female or self-fertile, so you might luck out and get both flower types on the same plant (I imagine you would still have to hand-pollinate when it's indoors though). If you only get female flowers, you'll need to get multiple plants to get fruit.

Thanks, fabaceae_native. It's good to know that it's at least possible to grow them potted. It seems a pretty plant even without the fruit. Most of the information suggested that it was going to be a plant it and build a greenhouse around it proposition. :)