Nice touch with the pic ;D
Here is my take...remember when you played road hockey, in the fall before the snow dropped, you couldn't slide your feet or pads in anyway possible without ruining your gear, or clothes, or some skin in the process. THAT is how you have to approach your game in a gym environment, kinda like you pointed out already. If anything it helps you think more about your angles and depth, not to mention some sweet '80s highlights
Here are some tips I found out when I gave gym hockey a shot...wear wool socks over your shoes, the cheap grey work ones, helps with sliding your feet across and in split saves. Wear steel toe shoes or boots to avoid that painful toe shot or slash. Finally, get some shorter pads, 1"-2" shorter. Since they are resting on a lower surface than your skates, it makes them rise higher and becomes cumbersome, your mobility will be that much greater.
Have fun!