Yeah, a major concern with putting synthetic through a high mileage original engine is that there are all sorts of sludge deposits that have built up over time, and the synthetic can dislodge these rather suddenly. This can end up resulting in chunks of crap going through your oil passages and into your critical components.
Compression test is fast and easy, a basic kit is cheap at $20-40, don't need anything fancy. You could also check at a car parts store that loans tools. There are multiple write-ups/instructions for doing a compression test, and it shouldn't take more than 30 minutes start to finish.
That compression check is key. Most of your sources of oil leaks (and pretty much all the main sources of burning oil iirc) will also cause low compression: Piston rings, valve seals, and head gasket. If all cylinders test good on compression, you have narrowed your loss of oil down significantly, and most likely won't have to do any major engine work.
Sticky rings are pretty common and result in burning oil and low compression. If you have low compression in one or more cylinders, the oil test will indicate if it is a bad piston ring(s). If it's not sticky piston rings, valve seals can be replaced with the engine/heads in the car (and valve seals are cheap!). Piston rings and head gasket, not so much...
I am curious that you haven't seen any patches of oil in your driveway... If the compression test (which will give you an overall health assessment of the engine) looks good, you could drive the car up and down the driveway, forward and backwards AFTER you have driven the car around and the engine is up to temp. Look for any dripping spots of fresh oil on the pavement. Perhaps you have a leak that only occurs when things are warmed up and in motion, for example an oil pan gasket leak at the front of the engine that pours oil under breaking or something.
Also consider that people have had oil burn through the PCV system under heavy (read autocross-style) driving. I don't know the details about this, but it may be something to consider if you drive like a bat out of hell.
To sum it up: start with a compression test!
***Edited due to being tired and needing editing... and sleep***
***Edited again due to valve seats having nothing to do with oil leaks, and I need sleep!***