Keep in mind that Solupay is both a provider of FirstData services (which you connect to either through Payeezy or NMI), and provides the bundle of customizations in NetSuite to use the NMI or Payeezy gateway to send payments to FirstData. What are you trying to do with you WooCommerce / Payeezy payments in NetSuite? Since they aren’t being paid through NetSuite, Solupay isn’t really involved, other than being the gateway provider.
Also, I agree that talking to Solupay and asking for any kind of documentation or technical details is just an exercise in frustration. They seem to have nothing written down, and rely upon tribal knowledge and getting the right person to achieve anything.
In our situation, we use Solupay within NetSuite, but also make direct payments to the gateway through an external application. We simply gather enough details to record a Cash Sale from those external payments, and send them to NetSuite through a Restlet we created. We use custom body fields to record the unique values we need for searching and reconciliation. This may not be sufficient for you, but was good enough for our needs.