Cameo in the citrust forum, with a naive question! Or rather, a bunch of them.

I have an orange tree - don't know what variety it is, just know that it produces oranges, and it's not a mandarin. I'm not completely clear on its age either, but the main trunk is about 3 inches in diameter, so I'm going to say 8 years or so since growth tends to happen almost year-round here. Due to interference from nearby, larger trees as well as some really atrocious pruning (with a weed whacker) by cheap, crappy landscapers (of which there are many in Phoenix, most of them aren't here legally in the first place) hired by an illegitimate property management company, the tree's developed a sort of anemic growth pattern. About 2/3 of the growth as well as bloom and fruit bearing is concentrated in 2 or 3 long limbs that project about 10 feet into the air above what was clearly once a well-developed, balanced mass of foliage (which doesn't seem to want to bloom much) from the tree's younger years. In short, it looks utterly ridiculous, and it's probably not very healthy either.

I've cut back the interfering tree as much as I'm comfortable with, as doing it too much would mean sacrificing privacy, and in January or February I'm planning tentatively on eliminating those prolific upper limbs of the tree. I'm hoping it will encourage new limbs to sprout once again on the lower portion of the trunk, or remove the lower branches from shade and allow them to bloom and bear fruit, at least. However, I've also heard warnings against pruning citrus at all, so should I even bother attempting this? Or would I just be crippling the tree even further?

And also, with all of this perfectly healthy scion wood after removing large branches, would there be a way to cleft graft them onto lower branches of the same size, like you could with other fruit trees, to help the process along? Or is that a ridiculous proposition also?

I'm from New England, I never had to know anything about citrus 'til now. I can include pictures in a follow-up if it'd help, but I don't have any at the moment.