The MUL doesn't have an availability listed in the Late Succession Wars. That's different from "extinct", although it's possible by the last sub-era (which starts in 3020), it's still going to be marked that way or dwindling severely in numbers. (Remember that the LosTech sub-era runs for 120 years, plenty of time for something once-widespread to go functionally extinct.) The book's talking specifically about the height of the Succession Wars, too. If you'd like the MUL Team to take a look at the final availability, post in the MUL thread in the Errata forum and we can dig into it further internally.
Of course, as I point out periodically, the MUL is a guideline and recommendation, not a straitjacket. If you want your mercs to have rusty, beat up old Tigers, they've got rusty, beat up old Tigers. One of the Wolf's Dragoons scenarios had a run in with a couple of Mackies centuries after everyone thought they were lost to history, for instance, and in the Succession Wars, the Mongoose is known to have individual examples in the hands of the Houses but they don't have access listed because it's one or two for each House.
For the record, Bulldogs are actually quite in character for an FS-aligned unit. The Suns bought a number of them before the Succession Wars for the same reason a lot of people bought them: It was cheap. They used a lot of replacement parts to jury-rig them, making it a logical enough unit to pass on to militias or mercs. After the Fourth Succession War, the FS also stole a lot of them from Ares but that looks like it's after when you're planning to set things.