How can I open a US Dollar account for my UK-registered company and use it to receive USD from Stripe and/or PayPal?

Mercury.co is another good alternative - a similar platform to Transferwise. It sounds like with your scale you will eventually need to open a USD account with a larger commercial bank in the U.S. (Wells Fargo, Citibank, Chase, etc). You can open a U.S. bank account for a U.K. company, even if the responsible party or shareholders don't have social security numbers (SSN) or Individual Taxpayer Identification Number (ITIN).

Unfortunately, it requires you to physically visit the U.S. and go into a branch office to open the account. I always recommend calling in advance to several branches and set up an appointment. Explain that you're a nonresident looking to open a U.S. bank account for a foreign corporation.

In cases where banks won't open accounts for foreign corporations, you can open a U.S. LLC (Wyoming or Delaware) that's 100% owned by your UK corporation. The US LLC can open the US bank account, and your sales deposits can funnel through those accounts.

Use Payoneer.