The tree is probably in a biennial cycle and it should fruit again next year on its own. What you can do at that point is thin the fruit early so it's not overloaded and that should get it back on a yearly cycle. You can prune it but that probably isn't what the problem is and depending on how you prune it you could hurt next year's production (like if you do the typical hack job of those who don't know about fruit trees and leave nothing there to fruit with). You should at least dead wood it. Other than that it's impossible to say what it needs without seeing it. It could need some heading back. It could need thinned.

We had a blockage at one point and pulled out tree roots when cleaning. The maple was only feet from the sewer line and it is a old house, so it is not surprising. The new tree will be planted further away from the pipe. I think the other trees on my street are lindens, but I'm so bad at identifying trees. From the bark, it looks like lindens from the pictures I looked at online. Also, I don't jump over these trees, but don't frown either if that makes sense. It isn't an issue the city is offering a tree and I'm happy they ripped out the maple (it scared me with constantly falling large limbs). I'm just going to use the tree as the base for designing the front yard and don't want to find out I based my plan off a horrible tree. Hope that makes sense. I'm just a little confused as some sites classify the these trees as medium trees and others indicate large. Maybe they stay smaller when planted as street trees?

Butchering a fruit tree should be done in winter while the tree is dormant, as I advised in my initial post. In the spring after the tree has expended it's stored energy into pushing out new leaves puts a lot of stress on the tree. It wants to start collecting the expended nutrients, sugars, and energy from the new leaves but once those leaves are cut off, it has to start over. That tree did, as you said, push out new growth again so the butcher job didn't kill it right away. Looking at the trees in the background and how some seem to still be dormant and others are just starting to push out new growth, I wouldn't discount the tree yet. I think its great you only like a natural growing tree. In my small yard, even a fruit tree on dwarfing rootstock will grow to 15' which is too large for my needs. I keep my trees manageable for what I want. The local avocado and apple growers have been switching from growing standard height trees to growing shorter trees with more trees in a spacing. Lines of trees that were on 20' centers have been cut to the trunk and another tree planted in between to create 10' centers and then the trees are kept to the 10-15' range for ease of picking. The trees are more productive per acre, and there is much less danger in picking them because the picker isn't 25 feet up in the air. I'd like to note that many of use here advised the OP to first thin the branches out to rejuvenate the tree and re-establish the apple growing wood. The option of topping the tree down to the trunk was extreme and not what I would do first, however it was an option should that fit the OPs needs. The question was if the trees were worth saving and if they could be salvaged. I answered with a resounding yes to both and stand by my answer. The trees can absolutely be rejuvenated and for you suggest giving up on that old of a tree because its old doesn't make any sense to me. We have many 100+ year old apple trees in my local mountains still producing fruit.

Wow 12 grafts and you want to do a dozen more! That's cool, have any of the other grafts given fruit yet? Just curious do you spray the tree, i'm just thinking it would be really difficult to do with a big one like that? Not sure about how much you should cut off, it seems like you want to take a good chunk of the tree off. Usually the rule I have heard is pruning more than a third off can stress the tree, not really sure how much would come off if you do what you say. I only have stone fruit, no apples but I was thinking if it were my tree, I would probably do it more gradually so I was thinking maybe top it to about 15-20ft the first year, and take off not all but some of the branches that put the most shade on the grafts. And then following year take off about maybe 5 feet off all around and clear some more branches which shade the grafts, and repeat the year after that. I think that way might be more of a better gradual way to reduce the tree size. But either way operate on it when it's dormant, preferably late winter before the buds swell and it leafs out.