Salesforce Exception Emails Don't Send

Has anyone else experienced this issue?

Yes. I've seen this previously with Apex Exception emails in When are unhandled exception emails suppressed and not sent? or Why do I not always get exception emails even though I've set them up?

I believe the answer there still stands. You won't currently get one-to-one emails for every unhandled Apex exception and the mechanism that determines which exceptions get suppressed and which get sent is currently not publicly documented.

Are their any suggestions of things we could try in regards to receiving these emails? (I'm primarily concerned about unhandled exceptions. We have the ability to monitor handled exceptions at the moment)

At this stage the only mechanism I know of to catch unhandled exceptions are Transaction Finalizers on Queueables. These provide a post transaction point that will detect the exception that terminated execution.

Does anyone have any suggestions around getting around the Premier Support paywall?

That is a much more complicated issue that I don't think we can fully address here. There are a number of community members that continue to advocate to Salesforce for improving the support for development related bugs without needing to pay for Premier support. It is often raised in places like Meet the Developers and True to the Core at various conferences.