If the tub is fiberglass, which most drop-ins that I have seen are, the body of the tub will have a little flex to it. Break out the tile, leaving a small section underneath the lip of the tub every 18" or so. Then use a prybar to "carefully" lift the lip up, and slide a shim between the section of tile and the tub. This should give you enough room to get the new tile underneath. Then, after the new tile has set, put shims between the new tile and the tub, remove the last few pieces of the old, and finish the job. IE, get rid of the wife, because it sounds like she is a HoneyDew fountain.