I bought a low cost 9" World Globe for about $10.00 at FEDCO. A larger size would also work. How to start. Assume you are only going to show the displacement or shift of continents most likely to move. I assumed the biggest continent (Europe) would not slip that much and if it did it would stay some what in the same basic shape as shown in Nancys New Geography map.
Start with the new south pole at the tip of India. Drill a hole for a pivot and drill a hole on the opposite side. I ended up with holes at about 77 degree west longitude by 8 degree north latitude for the new south pole and 103 degree east longitude by 8 degree south latitude for the new north pole. Next mount the globe back into it's mounts using these new holes. Take an electrical tape about 31 inches long and tape it down to some scrap Formica. Using an exacto knife and metal ruler make a cut the full length to make the edge of the tape straight. Now using the metal straight edge cut a strip about .1" wide the full 31" length. Use the zero degree Latitude marker scale that is part of the frame as a guide to lay this tape down, as you rotate the globe. This becomes the new equator. Another way would be to take a permanent marker and hold it on the zero degree latitude scale while rotating the globe.
Cut up patches of .003" thick clear plastic tarp. Thick plastic bags cut up would also work. Cut a peace that will more than cover the continent that you wish to capture by about 3"-6" extra around the perimeters. Tape it down to the globe over the continent around the edges at about 4-8 places depending on size. Use a hair dryer to heat up and shrink the perimeter so that it fits the round surface. It will melt and act like heat shrink tubing. If your hair dryer is not hot enough block some of the holes to cut down on the air flow. You can temporarily put tape over about 1/2 or more. Once you are done let it cool. The plastic will continue to shrink as it cools. If you start drawing right away your lines will be off as it shrinks. Once it's cool outline with a permanent marker the continent. Untape it and cut off the excess plastic. Set it aside and do this with each content you wish to move.
Once all are made tape down the contents so that they look the same as Nancy's drawing. Now if you get real ambitious you can attempt to draw using another color the shape that will end up taking into account some land going under the sea and some land rising. Do this for only the lands you are interested in.