I am facing a similar issue, with a similar setup but on Woocommerce, I︁ had Woocommerce Payments (powered by stripe) working on my UK LLC Setup, but since most︂ of my customers are from the US and I get paid in USD, I decided︃ to stop all marketing in order to reopen the account with my US LLC setup︄ (had to give some time between the last orders and closure of the account in︅ case customers requested a refund or opened a chargeback, I could respond to it.), before︆ the waiting period finished, the chargeback rate went up since the volume of new orders︇ was close to none and ended up with a suspended Woocommerce account..
I then contacted︈ Stripe to open a new account, explaining my situation before I signed up for a︉ new Stripe account with the US information. Long story short, the account got approved, and︊ a customer tried to place an order but was deemed a high fraud risk order︋ by stripe radar, their payment was blocked and shortly after, stripe decided to suspend my︌ account with the following email:
I submitted the EIN document and it was︁ rejected, I am now in the process of appealing that decision too..
As for the︂ proposed payment processors, Squareup requires an SSN to register which is not applicable for most︃ of us (non-residents), as for the rest, they're either a big hassle to setup, their︄ user interface is not very friendly, or they just bluntly don't accept this kind of︅ setup.
As for my business, It is a simple dropshipping business, except I source my︆ products from the US to prevent shipment delays, which is relatively less risky compared to︇ China-US drop shippers.