I've never climbed and LA7 over 9k once myself, and see the majority of players doing the same. So maybe that's what I base my opinion on. I have the same opinion of any F4 when in the LA7 as you do Sax of the LA7 when you're in the F4UC.
As Skyyr said, over 12k the F4UC may have an advantage, but I rarely if ever see the LA7 up there, much less higher. And even if it did, all it has to do is evade once, then dive/extend at speeds the Chog has NO chance at matching and reset and take back the advantage.
I'm not even that good and I have the exact confidence in the LA7 it its typical fighting alt as you claim to have in the F4UC. In fact, why not put Skyyr or Krup or another really good LA7 pilot in an La7, and you in the F4UC Sax, and split the duels, half at 12k, and half at deck to alt under 12k fields in the DA. I know where my money is going, and I'm still sticking to that 9 out of 10 advantage. The slimness of the advantage the La7 has is a little wider than you think it is, at least IMO.
I don't doubt your abilities or confidence against the hordes of noobs and mid level players in LA7s while you're in the F4UC Saxman, but I believe you in pretty much any F4U, or even in any fighter, would have that same feeling when you're going into a fight against them. Put a copy yourself in that enemy LA7, or somebody even a slight bit better than you, and I don't think that outcome is going to be quite so assured in your mind after a few DA sessions.
Just my experience and observation, some seem to agree, some don't. I don't have a lot of F4U time since the Chog went perk, so I admit I could be completely wrong, but I would need that to be proven, as I said, in some DAs with good DAing pilots (NOT me) in the LA7 vs you in your F4uC Sax. IMO pilot skill being equal or close, in the AH MA typical engagement alts where the LA7 lives, the F4UC is going to die virtually every time in a one on one fight.
Respects.