I'm not a fan of synthetic oil. No reason, just because they are more expensive. Never had an oil-related problem in 25 years of use on all types of engine. So why change. Dino oil works (well).
I don't see the relationship between type of oil and the leak. If it's going to leak out, I rather leak out the "cheap stuff."
1. Have you try additives to stop the leak? This comes to mind. http://www.prolong.com/A_ET.html
Not sure if it will work.
2. Time for a new car. $tart $aving up.