I'm not a person that generally requires all my floors to be at the same height but I think 1" is too much. My thought is that the average person should be able to handle differences up to 3/4". Over that it's a potential tripping hazard. I also judge transitions more harshly if it's in a path where guests might encounter it regularly. A guest is more likely to trip at a high transition. For instance, if this was from your master bedroom to the master bathroom it would be less critical.
How is the backer board fastened? If it's nailed you might be able to remove it and the two layers on top all at once. Also, how does the addition of 3/4" of flooring affect your cabinets and appliances? Or are they all being replaced?
Like I said, I'm not that picky about heights being perfect but if it's achievable I would want it done, especially considering the life span of a solid 3/4" floor. In this case If it was mine I'd suck it up and remove as many layers necessary to make them level. because I know I'd regret it later.

I think that's what we're actually going to do. I'm so compelled to "cut corners" just because I want this remodel done asap, but alas...I must come to grips with reality. We will be in this house for years. What's another few days of work?

sigh

thanks for the input!

I'd definitely spend a day demo-ing the existing down to the plywood subfloor. With a couple hammers and wonderbars it shouldn't be too terrible of a job. You're putting in a long-term floor, you should prep accordingly.

BTW, keep in mind that raising the kitchen floor could box in your range and dishwasher and make them difficult to replace in the future. Does your current flooring go all the way under the cabinets and appliances?