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Now some stuff I might need more input on.
I could use some help with references to see if there is already a English prescient. From the Five star stories we have the Jagd Mirage. In game it's called by J型駆逐戦闘戦士, a model type. I think Five Star Stories may have translations, in which case the classification types of the mechs would be nice. Otherwise "J-Type Extermination Combat Weapon" or ignore the obfuscation and go with Jagd Mirage.
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It's been a long time since I read Five Star Stories so my memory could be a bit off, but I don't really recall there being any formal classifications for the mechs. They all see limited productions at best and it's not unusual for any given design to only have one or two units ever produced. The narrative sorta treats each individual mech as a unique work of art.
Some are grouped into series though: Siren, Mighty, Engage, A-Toll, Mirage- to name a few. The Mirage series were the iconic designs of the manga- basically the ones that got the most model kits- especially Knight of Gold, the Mirage D. Jagd Mirage, was listed as J型駆逐戦闘兵器 while other units in the series were designated just letters, like the Rouge Mirage and Terror Mirage were A型 and H型 respectively.
All that being said, I have no idea which way you should go- I doubt either "Jagd Mirage" would mean any more to most people than "J-Type Extermination Combat Weapon" would. The former is certainly shorter and the difference boils down to the common name vs the technical one. To compare it with a different franchise, the famous "Valkyrie" transforming plane from Macross/Robotech is technically known as the "VF-1" but it's generally called by the common name of Valkyrie and rarely referred to by its number. Since they went out of their way to specifically use the less commonly referenced name, I guess that's the one you should go with.