Not quite sure if it was relayed (skimmed this thread TBH) this way, but when you extract you object, try copying itonto a new layer - a 2 layer PSD with a background and "the object".

Open THIS in Illustrator and drag the top layer (the object) onto the other document in Illustrator - people seem very click-happy with copy/paste but literall just get your Move Tool (black arrow) and you can drag any elements from one doc to another - just drag the top layer over.

Hope this helps-
-Lew ;-)