The answer to this question depends on how much oil the car was consuming. If it could run 2000 miles or more before it was a quart low; then the oil consumption was not related to the converter failures. 5W-30 is commonly considered interchangeable with 10W-30, as far as application suitability is concerned.
Even if the car was consuming an excessive amount of oil; I doubt that using 10W-30 or using a different brand of oil would reduce the consumption enough to stop this problem. But a bad PCV valve, or a bad fuel pressure regulator, could cause excessive oil consumption. Also, improper driving during the critical first 500 miles of the engine's life (not accelerating hard enough to seat the piston rings) or using synthetic oil before the vehicle had 5,000 miles on it, would also prevent the piston rings from seating. And that could make the engine use progressively more and more oil during its lifetime.
Many shops blindly assume that a P0420 code means the converter needs to be replaced. The fact is that this code is not directly triggered by the converter. Instead; it is triggered by the difference in readings of the oxygen sensors in the exhaust pipe upstream and downstream of the converter. If one or both of the oxygen sensors fail or lose efficiency; it will trigger a P0420 code. But many mechanics are either not aware of this issue; or deliberately replace the converter when it is not necessary, in order to gouge the consumer (especially if the car is driven by a female).
If you stand behind the car while someone in the car steps hard on the accelerator; there should be a blast of sound and exhaust pressure when the pedal is pressed. If there is a blast of sound and pressure from the exhaust; chances are the converter does not need replacment; and instead the oxygen sensors should all be replaced.