I’m not sure I follow…If the problem was diagnosed as a valve seal leak why do you have to put in piston rings?
I don’t like either option to be honest. I’d rather sell the car or trade it in and put the $2,300 towards a newer car with a warranty and no problems. Can you get a 2004 or 2005 certified pre-owned with a 100K warranty? Once an engine gets torn apart there’s no way to know how well the work was done. On the other hand burning lots of oil will present other problems beside just the need to add oil such as a clogged catalytic converter, coated O2 sensors, and unless you’re good at keeping up the oil level it will contribute to the oil sludging problem.