Yes, it is being installed perpendicular. I know it's not the ideal... but in the interest of time and budget, it's what we've landed on. We are likely going to do an engineered floor on top, to eliminate a little bit of the extra height. I would (just for my own knowledge on what to expect) love to hear the cons of this method, even if we're likely to do it anyway :) And it is a wood subfloor - so just add plywood ontop of that until it becomes flush is what I'm hearing. Thank you!

Demo. I'm never had bamboo flooring but, besides the concerns about making a moisture sandwich to rot and mold, I would be concerned about the expansion & contraction of the bamboo underneath the rigid overlay. What I understand about bamboo is that it is more wiggly than wood. Since you have engineered bamboo, probably doesn't move as much as a solid product would. There are other reasons to remove it--like avoiding having to undercut door casings and shorten up doors. Removing baseboard or compromise by having it buried behind flooring. Probably other reasons that I'm not thinking of, too. I would pry, scrape, whatever it takes to get it up & haul it to the firepit to get rid of it. There are going to be about a hundred responses telling you not to burn it. Fortunately, none of 'em know where I live. :-)

You are saying you DON'T like the first floor. So either REFINISH or replace it but not with a gray floor , please. .When I say replace, I mean rip it first. BTW, Stair to either a basement or a second floor can and probably should have at least a runner. You haven't shown the stair either, But a stair to a basement ? I'd probably paint the stairs Tread black, and risers white, and add a runner in a great pattern. If you want the look of the french oak everywhere, do it, and do it right. Rip.

Go for it. I would throw down some 3mm or 6mm cork underlay down (it floats just like the hardwood) and then float the hardwood. Use a high-quality joint glue on the hardwood and you should be fine. Besides...if it gives up the ghost in 10 years, would you be upset?