I think that for many reasons you would be very happy with a new, up-to-date MBA and that the various problems you've been experiencing would be in the past.... For one thing, software will run faster and more smoothly on newer hardware. There will be a bit of adjustment, though, to the ports being USB-C/Thunderbolt 3, meaning that you'll need to get a couple of adapters ("dongles") or buy new cables that have the appropriate connectors on each end. For instance, I am preparing to repurpose an older 5 TB external HDD for archival purposes now (actually a backup to another archival drive) and so recently got a Micro-B - to USB-C cable from Amazon to use with my 2018 MBP, as the original cable is Micro-B - to USB 3, which still works fine in my older MBP. This gives me the flexibility that I'll need for a while to work on and swap older files and folders around between the older and the newer machine. Since I've been shifting over the past couple of years to external SSDs for current backups and supplementary drives, I'm well-covered there and will be for the future, but they are still only 2 TB, which isn't sufficient for my ever-growing archival folders and files. Anyway, although some people grumble about the change in ports on the newer Macs, it all works out fine in the end after the initial adjustment period and figuring out exactly what one needs in the way of adapters and cables so that one can continue to use older external drives and other peripherals.
I would suggest right now with your current MBP that you think about not continuing with the beta program because that is actually throwing something extra into the mix -- more variables -- which makes it difficult to identify what is going on and to determine exactly what may be causing this proxy problem. It may or may not be a factor, but it's hard to know for sure, especially when doing the beta on an older MBP the way you have been. With the new machine once you've got things up and running to your satisfaction you could always resume participating in the beta program if you still want to do so.
Frankly, if I were me I would rather purchase a new machine BEFORE "something major" happens with the older one..... I assume you are backing up all your files regularly so that if a crisis does suddenly occur with the 2012 MBP you'll still have everything that is important to you?
