I don't think Kang v Cage is that bad. Annoying, yes, but not bad. Other than the fact that you're pretty much forced to take a ton of chip damage, you're able to punish or handle a lot of Kang's options.
A lot of times, I'll just chill barely outside his normal's range, and react to what he decides to go for. You can low profile most things he can throw out at that range (except for Low Fire, but the damage is minimal, and it's punishable on block, so if you're close enough they'll hesitate wanting to throw it out). Even tho it's difficult to punish Kang on block, I found its much easier to punish him on whiff. His advancing normals/strings don't move forward as quickly as Cage walks backward, so many times I can get the F3 punish for a whiffed string.
On Kang's wake up, I'll usually take a step or two back and use a D4. It'll make most of his armored reversals whiff and you can punish. Take the step back in case he tries to wake up grab.
On a read, you can punish both fireballs with a jump in. You can't do it on reaction up close because of Johnny's jump speed, but you get a free combo if read correctly.
Also, I'm not sure if the exact frame data, but I've been able to D1 out of Kang pressure after his D3 with mixed results. It either trades for Kang F44 or one of our execution is inconsistent.
This is a match up I've played a lot using all variations of Johnny, vs all variations of Kang. Despite FF having the parry, I think DF is the hardest to deal with. I'd also suggest A-List so you can get a full combo off of F3 without using meter. Stunt Double can work too if you're conscience with your doubles.
If this match up is disadvantageous at all, it's no worse than a 4-6. I think it's a solid 5-5 tho, IMO.