1) would not assume the engine is usable. you ran the car without oil.
2) if your current car doesn't have a ton of work put into it, this is a good route. take all of the aftermarket stuff for the new car. who cares what the market is like, you're getting a clean title out of the deal.
3) RS3s are pretty cool. your money.
Financially, option 2 is the smartest. You get a clean title, don't have to put cash into replacing it. You gain close to 20k out of the deal, vs. putting more money into an Audi that will likely depreciate as the market continues to cool.
If you swap the car or just build a motor, you still have a salvage title. A salvage title, swapped car will be a pain in the ass to sell later on. And you will spend much more on the swap than you'd think. Keep in mind your old motor might be worthless, which is a big hit to the affordability of a swap.