I am based in China and is non-permanent resident. So, my case is easier. Offshore capital gain is tax free as long as not brought onshore.
For my research done so far, I am considering several options, which may apply for you:
1) Use US based broker like Interactive broker or Charles Schwab for US registered ETF below a 60 KUSD as IRS would charge estate/inheritance tax above 60 KUSD at 45% tax rate. I pay 10% withholding tax on dividend. IB is cheaper than CS and allow investments in many markets but service is poor. On the other hand research and service in CS is outstanding. So, I am almost think to have accounts in both of them to get the best of each of them.
2) For above 60 KUSD, use Charles Schwab offshore mutual funds as not liable of either estate tax or withholding tax on dividend but the management fees is higher than ETF and actively managed and can only be traded through phone/email. Also, minimum investment is 10 KUSD per fund. So not as flexible but might be suitable for medium-long term investor and especially for fixed income/bond/gold funds
3) Use IB to invest in non-US registered ETF in non-us stock market. Therefore, I think no estate tax is payable. However, you will be trading in foreign currencies if your account is in USD. May-be one way is to have EURO account if you only trade let say in French stock market. I am not sure for stamp duties. I assume some stock market does not charge for it if trading through offshore broker.