I thought the current explanation is that they used primitive shuttlecraft type vehicles prior to the invention of the modern Aerospace fighter? The engines for those are at least built similarly to warship engines, if slightly heavier for their size. Mind you this does introduce a few other problems from a design standpoint. Do you then consider the Winchesters at the time to be outfitted with standard shuttlecraft bays(200T apiece) or do you limit the bays to a smaller/lesser tonnage but one more consistent with what would become standard Aerospace fighter bays(150T).
Also I just take those dates with a grain of salt. While I don't contest the Winchester as the first warship, we now know that the Taurian Toro(2481) and Talos(2532) both predate that Griffin 2534 date. That's even assuming they produced the Griffin at all. As I understood it "Star League designs" only started being built in the TC post RW. If the Taurians were already building Griffins(licensed from Earthwerks in Keystone, FWL, another hurdle I won't even go into) at this time, you'd think it would appear in the RAT's for the Reunification War. Checking.. nope.
RW RAT's specify the most common medium mechs most likely to appear in Taurian units of the time. It has the Dervish(ostensibly commissioned by LC but produced in Achernar, TH), the Shadowhawk(Lang Industries, Caph, TH), the Wolverine(Kallon Industries, Nanking, TH) and the Gladiator(the modern 4R version by Merryweather Industries 2490 - TC must have scooped up a huge chunk of the completed first and unfinished second production runs) alongside the native Talos. No Griffins.
Aerospace RAT's for the RW do show the Lightning, though not with the sort of frequency to suggest they were being produced locally (i.e. not more common than other designs). Except for the minor problem of the modern G15 variant not entering production until 2511. But fear not, the original G14 model did enter production with the Capellans in 2469, plenty of time for the Taurians to capture one and reverse-engineer it. I'd wonder why they didn't develop their own homegrown design, particularly since I don't see them negotiating with the Capellans at this point for a license. It's not as if their technology base didn't have what it takes to develop one, the Canopians were afterall able to put the Dragonfly into production, but I'd just be nitpicking at this point.