We replaced our laminate with vinyl planking last summer. The installers did not have to remove the ice machine line because there was enough length to work with it still attached, so you may want to check this out. Perhaps the gas company would remove and install your gas stove. We had enough clearance for the dishwasher because the new floor was the same height as the one removed. Having baseboard removed is a personal choice. Bringing the flooring up to the baseboard and using quarter round is also a nice look. And more importantly, it saves cost of replacing the baseboard, and the wall may be damaged during the removal. It's not realistic to use the same baseboard in most cases.
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