JaqFrost: You only get asked about the billing address in Europe because that's where the new VAT regulations have come into effect. It has no bearing on elsewhere in the world.
There is a CD-key for the DLC as well, which I can live with as long as nothing calls home or requires access to the Internet. I haven't installed the game yet, though, so I don't know if there's any online verification of that key.
Licurg: Haven't tried the DLC yet, but it's just a one-time CD key like in the main game from what I heard.
I use Paypal all the time with my VPN, and never had any problems.
catpower1980: GOG maybe doesn't ask for an adress (I pay with paypal so I don't know) but one way or another they are legally required to get your location infos with two pieces of evidence. Itch.io also implemented the VATMOSS pop-up on their website recently. Next to follow would be Bandcamp as they're still wishy-washy about that.
....
Also, bear in mind that using a VPN or a false identity could play against you as depending of the identifying pieces chosen, they wouldn't match and you'll be required to give more infos or your payment won't be accepted (I'm talking in general, not particularly about GOG or IGS cases).
Example: your credit card was issued by a Cyprus bank but you give an IP in USA => wrong
You can try to circumvent the system but it won't always work (as thus, you wouldn't be paying any VAT in fact).
Now that reminds me I have to fill my quarterly VAT declaration, urgh! :(
Thanks for the answers everybody! I'll probably buy the BTA too then, but proceed with caution at the checkout because of the risk of my payment not being accepted.
One last question though (sorry if I'm being annoying): If the CD-key is one-time (as Licurg mentioned), will I be able to install the game to another computer in the future (in case I change pcs or something) or does this practically count as a single-pc license and the game will only be able to be used at the pc I'll first install it? Becsause if it can work only on 1 pc, I'll have to think more whether this VPN business is worth the risk...