I need someone with knowledge of home central AC.

[bm02tj]

Some of the problem is Formicary Corrosion caused by indoor pollution mostly on indoor coils of copper and aluminum
If there is some charge left add a sealer and top up if empty replace complete unit including line set
$10 grand is more than it should be

 

[Bb70charger500]

Well if it is anything I had a new system installed everything but duct work $2200 has induction heat too. But different areas need different things I guess. But $10k sounds Insane to me!