My first thought is an Asian pear. Can you cut into a fruit to see if it has a stone or individual seeds?

There a lot different Buckeye trees family's your leaves match to some degree yellow Buckeye but fruit green.

The tree ID guides did tend to steer me toward buckeye because of the very unique palmate leaves. I looked up photos for Asian Pear and Buckeye and neither seems to be a match. I pulled a fruit off the branch and sliced it up to show one of the two seeds inside. You can also see the seeds in the previous photo of the fruit rotting on the pavement. The seeds are much too hard to cut through with a knife, and the meat of the fruit is about the hardness of an apple. I had to clean the one visible seed off with my fingernails after using the knife to remove larger chunks around it.

Here is a link that might be useful: Imgur gallery of the fruit

As I look at more Buckeye photos on google images I am starting to think that may be the answer - though only a small fraction of the images are a match this might be some variety not so well represented in the search.

Try a white sapote, pronounced sah poh tey.

That's definitely it!
(white sapote)

Awesome! That one might make my list a few years down the road after all the normal trees and bushes are in, along with a jujube. How close to ripe are they do you think and have you tasted one?

I haven't, and I'm not sure how ripe they actually get before falling off - but I haven't really tried to harvest and eat one. If you have the means to extract and haul this tree, it's all yours. (Guessing by your name you're in southern cal, I'm in the Carlsbad/Oceanside area.) I've been debating whether to remove it entirely or just cut it off at about 6 feet and try to keep it a more manageable size. As I have no interest in the fruit it's not really doing much for me.

Thank you for the offer. I fear that's a bigger project than I want to undertake right now and with a tree that size, probably ever. Best of luck with whatever you decide to do with it. Should you want to try one, the seeds and rind are inedible but the insides should have a custard consistency and you'll be able to eat it with a spoon.