Let me start off by stating that there is no better way than to remove the old and isntall the new. It gives you a fresh brand new starting surface. The company that is recommending this to you is the consumate professional and does it the right way everytime and does not want any chance that your new flooring will fail. KUDOS TO THEM ! That said, lay-overs are performed sucessfully everyday, but the are only as good as the existing flooring that is there, and if there is ever a problem, it very well may affect the new in a pronounced and visible way. You basically need a perfect vinyl installation that you jsut want to change colors or styles to do this. Personally, we rip them out on almost every job.

What product are you dealing with and what's your location? CA labor is much more expensive than TX. Luan normally comes 4x8 sheets. If they do not use a full sheet, you still get billed for the entire sheet.

I would ask why such a steep price for installation. Ask which order the kitchen will be put back together. A small room installation cost could work out because they use a "day" wage for small projects. I've heard of minimum charges of 1/2 day of work or 1 full day of work regardless of how long it takes. But I'm suspicious of this because the installer has MANY other things going on (or so I believe by your post). A person who is redoing someone's kitchen will often give a little so they can gain the entire project. The small space install only works if the ONLY THING s/he's doing is installing. And I never buy the 'nothing else needs doing' jazz. A sheet vinyl floor can have some WONKY substrates underneath (can look like a roller coaster ride). Sheet materials are VERY forgiving. A plank vinyl is NOT forgiving...at all. In fact, a poorly prepared substrate is GUARANTEED to void your warranty. And I mean 99.3% of the time the lack of prep is going to void your warranty IMMEDIATELY (before he leaves for home). I think you have some conversations coming up in the next few days. And to be clear for us, is this the SAME person who is doing the ENTIRE renovation?

Have them redo it with a better matching color. Also have them score the filler so, it is not filled to the top. Basically clean it off so the prefinished bevel is showing.