Have you ever considered transferring to SOC?I thought the JGASF were the SOC in this universe. They certainly carry the operations Special Forces would.
The mainstay of the SOC are black-ops operations. Spying, sabotage, assasination and that kind of stuff. I think that's quite a different portfolio from what the JGASF does.
I'd even go so far to assume that the creation of the 1st JGASF was more politically motivated than an attempt to create an elite fighting force, though luckily for the LSF it did turn out to be one.
And it also showed how well the Terrans and Cyrvans can do, when they work together (even though the support from the side of the CSA was lacking quite a bit). Though some Cyrvans would probably take it as prove that even Terrans can do well, but only as long as they have a Cyrvan telling them what to do.