Any mechanic that would rack up a $700 bill without your permission and say you can pay it off by giving him the car is an unscupulous bastard. Check Tx law, there may be a dollar amount above which approval is required before continuing. If so you can use that to negotiate possesion of your car.

I'd pay $50 for a tow (I'm assuming the engine is torn apart)to another shop and $70 for a second opinion before I'd write off a $5000 car.

If the engine is shot then yeah, I'd junk it at a yard or post it on a volvo classifed website "as is".

Good Luck
Scott