It MAY be possible to work something out if you deal with one of the multinational banks like Citi or HSBC but don't count on it.
To keep this sleeping corporation alive:
1. File the paperwork in Delaware every year and pay the fees there.
2. File a Form 1120 (the corporate income tax return) with zero income and zero expense. Technically a corporation has to file a return even if it has zero profit. Don't forget Form 5472 (foreign shareholder of US corp) if it applies to you.
Solution from this mess? Find a US partner who can co-own this thing with you. Then you have a US-based human as an officer/director who can do the footwork to open the bank account.
Meta solution to this mess: someone can start one of these things as a service for 10,000 people like you. This carries thermonuclear risk of course, which is probably why no one has done it.