So far the issues we've had
Fortunately, we setup a dev environment prior to moving production to 10.5.1, it doesn't seem this version is very stable or was tested prior to release
I tried the first issue you're running into and didn't see a problem configuring a wildcard certificate for Portal. What is the error within the logs on disk?
I do not know it is a wildcard certificate issue, that was just something that I read seemed a possible issue. But the problem is documented with the only solution being how to recover. Common problems and solutions—Portal for ArcGIS (10.5.x) | ArcGIS Enterprise
What is the actual solution to the issue? Why does this occur in two completely different environments after they were upgraded to 10.5.1 when the certificate work fine in 10.4.x. What is required in a certificate to make this not happen?
The solution is the one that's documented. You should take a look at the logs to determine if the problem is indeed certificate related. This isn't entirely relevant as you're using a wildcard certificate but a common reason why you need to go through the referenced workflow is the CN of the certificate doesn't match the hostname of the Portal.
What's documented is not a solution, it is a workaround so your portal is not completely broken. But once doing this, the portal still does not have the real certificate applied, it is just using the default portal certificate.
When the certificate is not valid, you'll run into that particular problem. Since the web server Portal uses is Tomcat, and Tomcat will block requests where the certificate is not matched against the URL, the only way to fix the problem is modifying the config-files manually. I would suggest ensuring the certificate is valid to use for Portals internal web server prior to importing it. If you can post the error in the Portal logs on disk, (obfuscated if need be), then that'll help determine what's going on.