Everything seems to map correctly except the membership type, which is in the payment field

Everything seems to map correctly except the membership type, which is nested under the payment element and integrated with Square. I'd like to sync the membership options as a checkbox/radio field in HubSpot. Possible?

Unfortunately, you cannot map fields in the payment integration. An alternative will be to create the type of membership using the basic fields and assign a calculation value to it.

Guide: How-to-Assign-Calculation-Value

You can do the calculation manually and submit the total to your payment field.

Guide: How-to-Perform-Form-Calculation-Using-a-Widget