Yes, all this is fully understandable. It means, you just need a bank account capable of SEPA (to accept payments︀ from European clients and to pay for the merch you purchase) and capable to accept︁ payments from your U.S. account.
Hence
1) With what bank you have a US account?︂ Some US banks, especially big ones, offer SEPA payments to their clients as well and︃ especially if you have some US business, too, they can onboard you, probably.
2) I︄ presume that the owner is also the director of UK Ltd, correct? Then many of︅ UK financial institutions (which offer SEPA in most cases) will not be much eager to︆ onboard you (with a non-resident director), it's true. Yet e.g. Wamo and Interpolitan Money are︇ worth checking.
3) As having European business, you will have reasonable chances with European EMIs;︈ yet you must go for a such that offer SWIFT as well (to feed your︉ account from the US). E.g. Zen or Paysera can be a good bet. You can︊ also try Paywiser, looks fine.
4) From non-european EMIs, Currenxie is well recommendable; I am︋ only not sure whether they are able to offer SEPA to UK companies (to EU︌ ones they are not) – but simply ask them 🙂