Cookie, the way to save money with a huge (single) tree problem, short of paying full price to remove it, is to pay a good tree service to prune the hell out of the top of it (like the whole top half of the tree), and take off any limbs over the house. Not cheap, but way cheaper than the full removal.
It almost never kills it, and if it does, you have years before you have to do anything again.
I have 6 100yo (or so) oaks (white and red) that have been majorly trimmed 3 times, but not for 15 years. It's great having a big limb hit the roof in the middle of the night and think I have intruders in the house. All of them are very healthy, but the fall cleanup is getting really old (just like me).
would be nice, but our burr oak tree has only 2-3 big dead limbs way up top and not many limbs total, but what limbs I have are HUGE and if prunned off those big huge limbs, would not work or help much. The tree splits in the middle about 10 feet up and is somewhat hollow in that cavern where it splits. If those 2 sides ever come down, they will hit either backside of our house being only about 35 ft away tree about 70 to 80 ft tall or more.
having gotten estimates of 3K and way higher to remove, I will take my chances and hopes in next 20 years or so of my life stays up. does suck though picking up near weekly smaller branches that fill up half or so of a 32 gallon trash container if gets windy out. It is dying no doubt about it but luckily once the lightning hit the tree only deadened that top limb it got hit on and not other limbs. If it deadened other limbs the next year then probably with not many bigger limbs up top would have to be removed.