Well I did say it "should be" fairly easy to remove
Obviously it's just guess work on my part as I can't see the situation and I don't know how old your laminate floor and kitchen units are. If it's proving difficult to remove the laminate flooring then I suspect that it isn't the more modern "click in" type and has been glued together.
But I still doubt very much that your kitchen base units are sitting on the laminate flooring, it should only tuck under the plinths and go up as far as the legs, unless you have a very old kitchen with integral plinths and no legs on the base units. Otherwise I'm almost certain that the base units won't need to be moved.
I know what you mean about the appliances having a tight fit and being unable to lift them sufficiently so that they can slide over the laminate flooring, specially if the flooring has expanded and cupped due to water damage. But TBH as it sounds that your laminate flooring has completely had it, I would just smash it out/lift it up with the use of a nail bar/crow bar and bolster. Presumably your appliances should slide out when that is done. And I can't imagine that the underlay/soundproofing is worth drying out and saving, easier to sling it and replace with new, I would have thought.