A Corolla I assume? And is it really a 3 speed?
I guessing that you are adding a quart of oil every 500 to 700 miles. This is high, but not so high that it would result in smoking. And despite what some people claim, all cars consume oil. See
Did you make sure the entire PCV system was open? The PCV valve meters air from the crankcase into the intake system. You need to make sure all the lines in the system are open (PCV to intake lines and the lines that provide fresh air from the outside world into the crankcase).
If you are only using a quart every 500 to 700 miles, I would not expect plug fouling as long as the usage is spread over all the cylinders.
Probably a waste of money. Have you removed the valve cover to have a look-see? Why do you think you have stuck valves? Stuck valves would result in poor performance (missing, etc.).
If the car has consistently been using a quart of oil every 500-700 miles for 45,000 miles, it is conceivable that this has damaged the catalytic converter (especially if you used the wrong type of oil), but I doubt it. It seems more likely to me that the snake oil you have dumped into the engine is responsible. Before I replaced the converter, I'd have the after-cat O2 sensor checked.
I'd recommend against just blindly doing a valve job. And I definitely wouldn't just tell a shop I wanted a valve job. If you are trying to address oil consumption, you would probably just need valve guide seals, not a complete valve job and I don't think you need either. Here is what I would do:
1) Carefully check the oil level to verify oil consumption. Do it in the morning everyday for a while to verify that you really are using a quart every 500 to 700 miles. 2) Check the condition of the coolant to make sure that oil isn't leaking into the cooling system. 3) Verify that the oil is not leaking out. Just because you don't see a spot where you park doesn't mean that the oil isn't leaking. Look under the car for signs of oily spots. 4) Verify that your problem is not related to oil sludge. You can check for sludge by removing the valve cover. If your car is a Corolla, it does not have one of the supposedly sludge prone engines. However, if the car has been poorly maintained it could still suffer from sludge build-up. 5) Try one of the high mileage oils (Valvoline MaxLife is one brand, there are others). 6) If you cannot live with moderate oil consumption, pay an experienced mechanic to diagnose the problem. Since you don't see any smoke at start-up, I doubt the valve seals or guides are your problem. It is far more likely that you have a leak, or worn oil control rings. If you have been using ...hmmmm... cheap oil, it is even possible that the oil control rings are stuck. But since you have already tried the miracle products to loosen them, I doubt this is the case.If it was my car, and the oil consumption isn't any worse than a quart every 500 to 700 miles, I probably wouldn't do anything expensive (assuming I didn't have the sludge problem). If you drive the car another 60,000 miles, the additional cost for oil will be less than $250. There is no way you are going to have the valve seals replaced for $250. BTW, Toyota considers 1 quart per 1000 miles to be acceptable for a car under warranty, so 1 quart per 500 miles for a 6 year old car with 120,000 miles doesn't seem that bad.
Ed