... I'm not 100% sure the expenses are going to stop soon (if ever). If a guy has to pay 2-10x what it costs in Kalifornia to make a similar repair, and he's asking if he should get out, or if the bloodletting is going to stop-- then I think it's a kindness to be honest, and say, "No. It's not ever going to stop, until you pay $8K for a new engine, and then it's still going to weep oil"...
Mark, your seemingly simple questions raise a whole bunch of issues that we've been kicking around for years here in the forum.
The VS that built your car went out of business a few years ago when the founder retired after over 30 years. He built more Speedster replicas than any other maker by a huge factor - a total of maybe 5000 cars. His key to success was selling a nicely finished car at rock-bottom prices.
When he started, that was relatively easy. There was a vast VW culture in Southern California, VW was still making beetles and new parts (in Mexico and Brazil). Quality aftermarket engines, transaxles, and parts were cheap and plentiful. Fast forward to 2015 and the whole landscape had changed. For reasons too involved to get into here, VS quality started to slip.
Over the years, there were hundreds (maybe thousands) of VS customers who received relatively trouble-free cars. But towards the end, stories like yours became more common. I bought a new VS in 2013 and after many problems decided to keep the car but replace both the engine and transaxle with units sourced from local builders. But I was very fortunate to find a great local VW mechanic to walk me through all of that.
I get from your post that you'll be relying on a mechanic to make decisions about how to solve your problems and to do the actual work. I also sense, like others have said, that the prices you're being quoted are high, and maybe exorbitant.
Before I wrote any $1000 checks, I'd do some research with the local air-cooled VW community to find a competent mechanic and, at the very least, get a second opinion. In a town the size of Atlanta, there are bound to be some experienced mechanics who specialize in air-cooled VW's and some VW clubs who can get you hooked up.
Unfortunately, the bottom line is the one outlined in yellow in Stan's post above. Your engine may need some serious work, and it may be best to start over with a new one from a skilled, local builder. And that will cost some serious coin.
And, even after that, in the long run, these are nothing like modern cars in terms of reliability and comfort. You can't just change the oil every 5000 miles and forget about them like a Toyota. If you're not willing to think of them as an 'adventure' that requires some involvement and probably getting your hands a little dirty, you'll likely always be frustrated by the whole experience.
You're getting some honest, maybe painful advice here. Find some local help, think it through, and decide if this is really what you want.
A lot of us have done that and decided to play the game. But then, we're all a little crazy.