How can I get a patient’s orthotics covered when I’m not a Medicare DMEPOS provider?

You cannot. Only DMEPOS providers can submit claims to Medicare for processing (be they paid or simply processed as Patient Responsibility). While you can provide a form for the patient to self-submit, Medicare will still not pay this claim and the patient will be forfeiting their opportunity to self-submit reimbursable claims in the future. If you are a non-participating provider under Medicare then you can elect to do the same and enroll as a non-participating DMEPOS provider and simply submit these types of claims with a GY modifier.