I can't afford to have my account frozen and be told that I must fly to Europe to unfreeze it.
I may find you some options, but nothing will give you a guarantee that there will never be an issue that the bank will require a personal visit to solve it. Even if you open it without visiting the branch, and it works for some time, law and/or bank policies may change and at some point they may say "we are sorry, but we need you to come to our branch and sign this paper in the presence of our employee to continue banking with us". This will never be a completely unreasonable requirement, and because hardly anyone ever has a account in Europe without being here physically, if a bank places such requirement it won't give bad publicity, because you'll probably be the only customer of the bank for whom it is a problem. Even if at some point they decide to stop servicing you, it won't be completely unreasonable for them to say: "Sorry, because of legal changes we cant continue servicing you, you are welcome to come in to any of our branches to pick-up your balance in cash". Cash in branch is a most legitimate form of refund, and nobody will see it badly here if a bank does this to someone.
You can try something from http://www.offshore.barclays.com/
but even if it works, it'll probably require very high balances and be very expensive.
I think even non-EU offshore Barlcays accounts have SEPA-accessible numbers.
If you don't want to risk flying nor the Barclays offshore would work for you, nor HSBC accepts you, then you'd be better-off partnering with me, and when you have someone who wants to pay with SEPA, you contact me, I accept the SEPA, convert to USD and send a USD wire to you, and in exchange you do the same for me - when someone wants to pay with US bank transfer I can't accept, I can ask you for the same thing in the opposite way, with the difference that I will want a USD wire to my account in Poland.
If you want your own account, there is a bank http://www.sync.pl/
in Poland that would not require ever visiting the branch, as they service customers in Poland that way too, they have virtual branches with video link, and don't service anyone in physical branches, you can be a foreigner and have a foreign address, but:
1) you first need to have an account at any other bank in Poland and make a transfer from it to verify your address - and to open that you'd need to come here
2) you'd need a polish ID number PESEL, which you can get as a foreigner if you even temporarily live in Poland even for a short time.
Getting a PESEL number requires a temporary residence permit in Poland probably.
Your Sync account will not be tied to the address you get your residence permit in Poland for, and you can use your US address together with the polish PESEL number in Sync without problems.
So come to Poland for three months, get a PESEL number, open one bank account at any polish bank, then open a http://www.sync.pl/
account, make a transfer from your first account to Sync to verify it, and then you can fly away back. Its a nice country. That way your visit will only be for the first bank account, which you will later close, and you will never have visited the Sync Bank which you will keep, so they will never be able to make the assumption that you can come to a branch to fix things. They don't service anyone in branches anyway.