Janet, I don't think it would hurt the tree to prune it after flowering, if you don't really want the fruit. Another option is to thin some branches out, and / or to prune off some of the early small fruit, so you have less but perhaps bigger better quality fruit.
If you do let the tree bear some fruit, I would suggest putting a sign or an ad (maybe freecycle or craigslist on the internet) offering for folks to come pick it. You can even charge a small fee and have them bring their own bushel etc.
Laurie

Laurie, thanks for your suggestions. In fact, I did run across a couple of ads on CraigsList from folks who wanted fruit, so I called them and invited them to come take all they wanted. That should take care of this year. I wouldn't mind enjoying the blooms in Spring, but I sure don't need this much fruit next year!

janet

You might also consider contacting your local food bank. With the costs of food right now, I'm sure that they would be happy to get volunteers over to pick clean your tree to provide fresh fruit for the needy.

Wow! I so wish I lived near someone with that problem! I just moved to a tiny yard with no fruit trees in the neighborhood. Our last house was across the alley from a large tree and I would clean up all the wind falls in exchange for all the apples I wanted. Great for both of us! Maybe you can find a "fruit nut" that lives near you!