How can a non-resident obtain a high-risk merchant account in the US?

If your acquiring needs are from the US, then you need to incorporate there. Simply register a company in the US (Delaware or Wyoming), an LLC would suffice, obtain an EIN (Employer Identification Number), and get a bank account opened. Various firms can assist you in opening your company bank account without ever having to visit the US.

Once you have the company + EIN + bank account, you can then apply to literally 100s of merchant providers and ISOs who deal in high-risk acquiring.