A few ideas:
I'd go through the various drives with the input gain down all the way and just shape the tone, boosting the treble and bass to suck out the mids, to kind of simulate the higher resonant frequency of a single-coil; don't boost the level of those pedals either, in fact, experiment with the drive level pretty low. Or, try just really messing with the input EQ in the amp block until you get that pick attack to get more of that stratty sound. I used to play an LP only, and I would go the drive route to get as close as possible. I don't know which drive would get you there in the Axe FX, but there are so many with wildly different tone controls, I'm pretty sure you'd find one that would fit the bill.
One VST option would be to try Blue Cat's Re-Guitar. That's designed to replace the tone of your pickups with those of a different design altogether. You can try a free trial.
Then there's the hardware option: the Keyztone EXchanger. I think there's discussion of that on this forum, so some people may be able to offer their experience.
Then of course, lastly, maybe trying another kind of humbucker that's designed for a good split sound, like some of the ones made by Rio Grande Pickups, e.g. But there are others out there. I'd be extremely keen to try ZexCoil TriBuckers. Maybe you can find an example of someone using them for slide. All the clips I've heard of their single-coils are fantastic.
Best of luck on your quest!