You don’t need to be a US citizen to get a US bank account. The bank I used was PNC and they asked: US citizen, US permanent resident or nonresident alien. For nonresident alien, they ask a few extra questions about affiliation with foreign governments or receiving payments from such entities, etc. Do note that these questions were all face to face, in person, during a trip there. They need 2 government issued IDs, one can be a Singapore DL.
But honestly — it is not worth the hassle to do all that. Even though PNC offers free domestic wires, mailing in a check is easier and doesn’t cost anything more. I was using TransferWise to send the money to PNC which incurred a similar loss on exchange rate anyway.
If exchange rate is your concern, I don’t believe you can beat trading the currency yourself directly in the forex market with IBKR. It might be worth exploring whether IBKR to TDA funding is possible. I would guess IBKR LLC should be able to wire, maybe for a $25 fee (typical fee with US brokers), but not totally sure.