As you can see in the image, I've done exactly what's in this video (although I used a square because it's way faster);
http://postimg.org/image/5p4psi5v5/
essentially this is how you do it;
layers 1+2 are your shape layers. these will be whatever your internal shape is going to be. in your advanced output make them whatever you want
layers 3+4 are your border layers. make these about 10-20 pixels larger on every point than layers 1+2
layers 5+6 are your background layers. they'll be the same size as your composition
please note, I'm ONLY editing the points on the output slices. the input must be the entire comp
in the advanced output you'll need to set each slices input source to the various layers
to change content, simply fade between layers in the appropriate shape area. Alternatively you can set up a bunch of columns and switch those instead, in that case you'll only need 3 layers.
Note; fading out the opacity on the shape layer will reveal the entire image on the border layer and so on backwards through the chain.
here's a more complicated image (only used 3 layer slices instead of 6)....it'll require more tweaking the more points you add to the output map;
http://postimg.org/image/47v3toh47/
complex shapes will also warp the internal image, but without more advanced masking in resolume it's the closest you can get using just the software!
can I haz prize now?

(please say it's resolume swag!)