I agree on papaya being a great thing to grow for winter fruit. They load up during the summer then fruit ripens during the time when less fruits are in season. There is less wasp pressure in the cooler weather. The past few months I am selling up to 100 pounds per week. I had many volunteers so I didn't grow from seed this year. That has turned out to be a problem as I've found the volunteers load up with over 100 pounds of fruit but are so superficially rooted they break off or topple over. I've lost 8 trees some have been propped up when they started leaning but still broke under the load.
I agree to grow good vigorous trees from seed, I have not seen very productive trees coming from nurseries.
Papaya grows very fast and the seedlings really have a short window in which they MUST be planted for success.
Those found in nurseries have almost always been held too long and lose their vigor.
My best results have been planting seeds in small plug pots or maximum 1 gallon pots, then before the trees get over one foot tall do the transplanting. Be sure to grow in full sun to keep them short and not reaching for sun.
If there is a chance of standing water you need to plant on a mound, many fail during high water events. My best results have also been by planting the trees deep, up to 1/2 of the tree being buried. They make adventitious roots and get a better foothold that way.
At the tropicalpermaculture.com site they suggest planting a handful of seeds in place and selecting the best six.
This is what happened for me on the volunteers. A dropped fruit rotted out and the seeds all grew and I selected from those. The problem is they get crowded, grow thin, and didn't develop very good root systems. Some also grew crooked which adds to the stress on the trunk when they load up.
When I say "load up", I am meaning that a highly vigorous papaya variety has the genetic potential to set 2-3 flowers on a panicle instead of just one. At that point the tree has 2-3 times the fruit on the same tree.
One last point is that my best papaya have been from the professional hybrid seeds. One advantage is that out of 200 seeds I have never had to eliminate a male plant, all were either female or hermaphrodite. The hermaphrodite fruits are longer and have thicker flesh. My favorite has been "Red Lady".
https://www.shop.alohaseed.com/product.sc?productId=17&categoryId=4One of my best. It continued to set even more and lived two years till it was too high to pick even with a ladder.
This is the potential: