Honestly, I'd recommend against using false addresses. There are brokers who are more international friendly, I have actually used Interactive Brokers and Schwab. Schwab offer commission-free ETF's that cover most of my needs, Interactive Brokers offer any ETF or stock at 1-2 USD per trade (there's a 10 USD monthly minimum if your assets are less than 100k though).
The main issue with Schwab is they charge around 1% for currency conversion, whereas Interactive Brokers offer almost-free currency conversion. Hence Interactive Brokers are often the best choice for international users.
However, there's one more pitfall: EU requirements mean that EU residents can no longer buy US-domiciled funds or ETFs. (FATCA meanwhile prevents most US citizens from trading in Europe, not that you'd want to because of PFIC.) I don't live in the EU so I'm not affected, but you'll want to research this carefully. I'm guessing you wouldn't run into this issue if you open a Vanguard account with a US address, but Vanguard are likely to block your account from trading as soon as they realise you aren't in the US (I don't know if they're one of the institutions that looks at your IP addresses to figure out where you are).
I suppose what I'm trying to say is: you're in a bind, and your solutions are either to get rid of the cumbersome citizenship, move to a country outside the EU (there are a few of those in Europe), or lie to your broker and hope they don't notice you're lying to them (at which point they stop you from trading).