I rate it as a very good Second-Rate Dogfighter. Frankly, for First-Rate the Eagle/Transgressor clones stand alone. The meta for Introtech ASFs is to accept some heat for a devastating Alpha Strike in the head-to-head pass. As such, the Stingray is built to heat up with the LLs and PPC, then cool by removing a primary weapon or weapons in favor of the MLs until it can safely hit the Big Red Button again. As long as you fight it the way it is intended to be fought, it is an extremely effective dogfighter.
The catch is that at +5 heat you get a random movement check, which can kill you if there's something nearby to collide with like a planet, an atmospheric boundary, a dropship, your wingman, etc. Mechs don't really worry until the gunnery penalty at +9 unless -1 movement loses them movement modifier and they can't resort to jumping.
A Stingray builds +6 heat firing the three big guns, which means random a movement check. It may have been better under AT2 if those rules didn't have random movement checks, but under TW it's flawed. Most things are with the way wing arcs changed, but the Stingray is flawed in a way none of the others save the Chippewa are.
In your place, if you have a factory for Rampage engines and think you can tool up a factory given specs, I'd try to convince Katrina to turn the screws on Bauer Industries to get them to sell the license if they can't or won't build the things. All the advanced tech Rampages have a 340 XLFE that lets you do a near-Royal version. Drop one heatsink it arguably doesn't need and the Artemis ant the armor can go up to Eagle/Transgressor levels. PPCs (as the original had) can be freely substituted for the LPLs if those aren't available.
Fairchild Dornier's Samurai is another nice out of production design by a Lyran company, though one where I'd look more at selling them the tooling since they don't build it for the very good reason that their factory got blown up. And I don't think you have the right engine unless you divert 300 XLs from the Phoenix line to replace the 250 standard.
Another option is to try to get the rights to make Chippewas or Thunderbirds, which may be able to be scaled up or down to use the Orca engine more easily than an entirely new design could be created. The royal T-bird is a dual Gauss design so making it into an Orca clone may not be out of the question.