First, our opinion about the flooring. We would remove the tub, the toilet, the range, and other appliances on top of the finished floor, install sheet flooring and then put everything back.
There are many reasons for our recommendation, but the two most important are: 1) sheet flooring is difficult enough to install without having to work around or under appliances, and 2) even though it is more difficult to install, a sheet floor is far more water-resistant than one made up of individual squares.
This doesn't mean that you shouldn't use the squares if you choose they can be beautiful. But, when the tub overflows there is a certain security in knowing that you went the extra mile.
A piano dolly is very inexpensive to rent and could be the solution to your problem.