About how many miles can you go before you notice it being a quart low? 1000 miles a quart, 500 miles a quart, worse? How many miles at on your Corolla?
Synthetic is a great oil, but it will not necessarily make the engine "last" longer - there are definitely pros with running synthetic, but if they are worthwhile? That is completely up to you and your situation.
- As mentioned, high temperature stability, harder to oxide synthetic oil, leading to deposits. But in the case of a car consuming oil - switching to synthetic may or may not do anything. In cases of heavy oil consumption - running synthetic only means you are spending more money on oil that will only get consumed in the end. They also tend to run thinner - so this can also cause an engine that hasn't been consuming oil to start losing oil. Not really a fault of the oil - just that the oil can now slip past the rings and get burned up.
- Also mentioned, synthetic tends to have higher solvency - wants to clean off deposits, sludge, etc., tends to run a little thinner, flows faster. Can be a good and bad thing - in a car that is leaking oil (older car) - this higher solvency can actually cause more oil to leak, as the crud and deposits are actually helping "seal" those leak points. In a modern engine - more solvency tends to be better - especially in the case of the 1ZZ-FE, as some of the 8th gen Corollas/Prisms have seen oil consumption due to clogged oil return holes on the piston. Running a thinner here is a good thing, gets in behind the oil ring and tries to eat away at those deposits. But in some advanced cases - even higher solvency won't help.
- Synthetics big claim to fame is low temperature flow. Subzero weather - when starting the car, it may sounds like it has molasses in the engine - with synthetics - it will crank more easily and get oil where it needs to go.
As for your use of high mileage oil - I'd continue to use that. Many formulations of high mileage oils are actually semi-synthetic. Some like, Castrol GTX HM and Valvoline Maxlife HM are some of the better oils out there. They do then to run on the thicker side of their viscosity range - which could exacerbate your oil consumption. On the 1ZZ-FE, some owners found that running a thinner oil, but still within the recommended grade - helped reduce oil consumption. Good example of an oil that tends to run thin is Mobil 1 synthetic. My usual go-to oil on my cars - Valvoline Synpower synthetic is another.
Doesn't hurt to experiment with oils - as each engine is a little different, some tend to prefer one brand/viscosity over others. The big key is not what kind of oil you run, but how often you change it. Your oil change interval at 3000 miles is pretty short and conservative - I wouldn't be surprised if you could run it out to 5K miles easily. But in the case of oil consumption - keeping an eye on the level of oil is the most critical thing. Your sump doesn't hold a lot of oil - if you end up suddenly down a quart or two - that remaining oil has to work a lot harder to protect your engine. So 3000 miles might be right for you.