This could help you in some way…I quite often morph objects by overlapping their layers by the amount of time i want the transition to take place. Then keyframe the first object with a fast blur to increase over this transition period & take opacity down to zero. At the same time blur and fade the the second one to come appear. Pre comp these layers and add a matte choker to the new comp. Adjust the levels of the choker till you get the required settings for a clean transition animation. There is no reason you couldn’t apply this as your circle falls into the floor and again as a rectangle rises from it.
Hope this helps! I saw a tutorial doing something similar once on youtube but can’t find it now, you may have better luck searching, it’s handy trick!