Subfloor repairs/replacement for kitchen remodel
We just tore out all our kitchen cabinets, flooring, and a wall to boot. The original cabinets (which we think may have been fabricated by monkeys, as they had more nails in them than Home Depot has in stock - and which were also nailed instead of screwed to the walls... but I digress) sat on what appears to be a basic plywood sub-floor. However, laid around the cabinets was another plywood sub-floor. On top of that is the original kitchen linoleum (house was built in 1968).
So what we have is a sub-floor at one level, another sub-floor on top of parts of it, and linoleum on top of that. We don't want to mess too much with the linoleum due to the risk of asbestos, so planned to lay new flooring down over top of that. But I'm wondering if this will be possible to do given the two different levels we would have to contend with (first level to bring the base sub-floor up to the level of the next layter, and then to bring up to the level of the linoleum - which of course, isn't very thick).
We hope to do either a floating cork floor or ceramic tile. I know that for both applications, it's imperative to have a level base on which to place the floor. But I'm wondering what the best options are for getting to that point. Should we take out the top layer of sub-floor? Should we bring everything to one level, and then put another layer of plywood (or some other underlayment) over all of it? Any ideas?
Thanks in advance for your help!