Hello, and sorry you're having problems. We are now connected on this website- which saves you money over having a Tech come to your home, and in many cases we can fix the problem you're having. In other cases, these things do require additional parts to fix. But I can help you with that as well.
The green tint is indeed a failure of the Light Engine in the set (the optical block portion of this component). Offhand Sony will not cover any portion of this- as there was an actual Class-Action suit for this exact issue, that's been closed out for about 5 years now.
To fix this issue requires replacement of the Light Engine- which in MANY cases can be purchased for around $400- if you're looking to perform the work yourself. Otherwise, your $650 estimate is right in the ballpark of what a shop will charge for this repair.
If you need further help, I can search for this set's specific light engine, but will need the full model number off of the back of the set to dig deeper (they did not all use the same model light engine).
Feel free to reply back if you need more help, or want to reply back with more details. It does not cost you anything more to reply back once you've rated. Please do rate me positively (at least 3 STARS) and I will continue with you until this is sorted. The positive rating ensures I am credited for my work.