I don't have nearly enough experience against Axl, but my general idea when I'm trying to get in on him as Zappa, especially if I think he's gonna do the rensen/rashousen mixup, is to jump forward and FD-- A little tricky to do, but it's possible to get the vulnerability frame down to 3 frames, even a 1 frame jump if I'm going really fast and desperately trying to get it. Though 1 frame jumping won't net me good forward momentum, it'll ruin the ambiguity of the situation-- If it's a Rensen, I block it. If it's a Rashousen, I can get over it and go for the punish. The issue with this idea is that the Rensen follow up can just toss me right back into the corner even on block, so Axl gets massive options off this.
I think the only SOLID option for most characters in this situation is to try to Instant block one of Axl's attacks and reversal punish, particularly any of his chain moves (though good axl's will cancel off the first attack if they expect this to keep themselves safe-- I saw you doing it watches). This is especially true with Zappa who is willing to get a trade from full screen on say, 2A, just to get some orbs and possible get inside, as 2A counter hit doesn't offer as much penalty as getting hit by Summon counterhit, which leaves Zappa at an advantage (free oki and 3 orbs potentially). Likewise, this is why using 6K or 5A against Zappa is bad, as he can just run under them and hit the chain with summon for free punish depending on his spacing (6k he'd just try to hit axl, mind you). The idea against Axl is that Axl is only dangerous to Zappa if he can keep the distance to what he wants, but if Zappa gets in close, Axl is in a tight spot. Zappa's mixup and shenanigans make Axl's counters practically useless, and trying to guess which benten to use to keep yourself safe is ambiguous at best. This ends up leaving a very weird matchup, where Zappa actually has more power than his opponent for once, but lacks the zoning tools he needs to do much with it-- Even the ghosts can become a liability if the Axl has meter to super punish them.
This situation is an interesting cycle that Axl can perpetuate ad infinitum if he so wishes-- Zappa vs Rensen/Rashousen is pretty weak, because jumping can put him back where he doesn't want to be even if he blocks it, and Rashousen obviously can catch him off guard if he tries to wait it out. So a smart Axl will abuse this against him, but an even smarter Axl will try to bait the Zappa into the punish-- He's gonna try it-- and get that free 6K once Zappa jumps, especially since Zappa is terrible in the air.
The only time this situation becomes in Zappa's favor is if he has the dog either between them or behind Axl, or if he has Raou to get a fast 5HS/6HS hit depending on distance to put the heat on Axl after a blockstring or after rensen block. The reasons why Zappa gets the advantage here should be obvious. If Zappa has the ghosts, he can do P toss in hopes of tricking the Axl into continuing his attacks and getting hit, which gives him pressure and frees him up to move as he wishes. The sword is weakest in this situation but can net possibly the best rewards if he guesses for his punish properly.
Obviously a lot of this is specific to Zappa, but some of it can be related to other characters as well-- namely, anyone with a reversal can do any of the reversal options Zappa has can do something with it. Especially DP's need to be kept in check by the Axl, because otherwise that shit will just ruin his day.