You can pre build the casings and install them provided you get really good measurements. Shimming is almost always required to keep things in line and tight until you get your case molding on.

LOL @ the cats! I'd suggest you glue and screw the window stool onto the sill/jamb from underneath using pocket screws. If you don't know what pocket screws are, just google Kreg pocket hole jig. The single hole jig and step bit are about $20 in stores. You'd want to use 1 1/2 screws to attach 5/4... 1 1/4 screws to attach 3/4. IMO the crown would look a little strange. A standard sized apron to match the casing would be fine, I would think.

HAHA I can't believe by typo. The weight is correct at 28 LBS TOTAL. But it's just 2 cats (NOT 32) at 14lbs/ea. My only concern with the standard size casing is with the 2 square stock underneith the stool, the standard casing might not fit over it well. Also it might look strange with the stool sticking so far out into the room with nothing under it. I guess I could just mock it up and see what it looks like but I don't want to buy all that crown without knowing. Anyone know where i might find some pics?