A few days ago, three separate sources pointed out Unknown Song #43 for me at more or less the same time (José Teixeira on youtube, Craig-UK/Craig L on this site, & another guy I've been having private email correspondence with). US #43 is "Hard Attack," by Fabien Chevallier, Christian Poulet, and Jean-Yves Rigo. It's the first Primetime track I've encountered on the Kosinus Label, which—as you can probably guess from the artists' names—is a French production-music company. I can't find much info on said artists, but I did notice that Poulet & Rigo are usually credited together. Unfortunately, the album—KOS 24 (Metal Warrior)—is one of only a few Kosinus albums to be missing from the online streaming services. You can find Hard Attack if you search "WCW Ultimo Dragon 1st Theme" on youtube, however.
*EDIT* - After finding an eBay listing for Metal Warrior, I found that only Poulet & Chevallier are credited for Hard Attack and not Rigo.