Jason

I think I may have found the issue. My hosting provider, in trying to diagnose another problem in Blesta, had turned on debugging. I turned it off and did a test run and I think it is working correctly now.
Not sure why turning on debugging would stop the payment process from working, but I think that was the issue.
Appreciate your help!!

Just in case anyone ever runs into this type of issue and is looking for a solution. The problem ended up being an issue on Namesilo's side which they have fixed.

We were able to figure out the issue by determining that:
1. The domains at the old registrar could indeed be transferred by manually transferring one of them into Namesilo. Thus eliminating the issue of the old registrar not releasing the domain.
2. We sent a properly formatted API call via SSH to Namesilo bypassing Blesta. We grabbed the error code/issue from the Namesilo API response.
3. The response was basically saying we had already started the transfer when we had not. So we contacted Namesilo's support and they were able to fix the issue on their end.

Thanks to @knownhost for their help on the server side narrowing down what the error code actually meant (FYI, having the actual error code/description listed in the Blesta admin side would have saved a lot of time with diagnosing this issue) and thanks to @namesilo for their help fixing the API issue.

 

Just in case anyone down the road runs into the same issue ...
I never really found a solution to this issue. I did get NameSilo working by not including a payment ID and instead have it default to using account funds deposited with NameSilo. I think there must be a bug either in the module or the API that isn't parsing or sending/matching the payment account ID correctly, but at least it allows me to put in orders now.
 

For anyone else running into this issue, the solution is to not create a package using the normal Blesta dialog, but instead click on the "Manage Packages" button when adding an account to the NameSilo Module.
See attached screenshot.