First off, many thanks to Robert P for his efforts in helping me. As well as Daniel.
The problem is now fixed. And I figured I would post it here in case anyone else runs into this issue.
I updated to 10.14.3 (I was on 10.14.2, and thought I had installed the newest update, but apparently did not). After recognizing the discrepancy from Robert's post above.
As suggested, I searched for a new driver from the HP website. Turns out one was available back in Sep 2018.
Before installing the new driver, Mac OS System Preferences under printers and scanners showed that driver version 2.0 was installed. The HP website showed 2.9.XX.XX (2.9.something) as the newest available one.
I downloaded the driver updater, and followed the steps. Nearing the end, the updater said that I had the AirPrint driver installed, and that it was recommended by HP to use the HP driver. I switched to the HP driver, and completed the process (2 more steps of verifying a page printed, etc.).
Once complete, I opened Dorico and my Font test file, and it worked.
The AirPrint driver I am not 100% sure how I got that on there (maybe trying to print from my iPhone years ago?). However, this problem is now solved provided I am using the HP Driver.
Dorico Pro 2.2
Finale (since v2.2), Sibelius (v1.2 through 7.3),
Mac Pro 2.7 GHz 12-core Intel Xeon E5, 64 GB RAM, 1 TB HDD