I dropped my Z3 and broke the battery door. Where can I find a replacement? The camera functions with a couple of rubber bands holding the battery cover down, so it loooks like I didn't hurt the functionasllity.

I had this same accident befall my Z1--
Simple fix: I bent a nice looking piece of Chrome plated rod.. (from an old grill that I had dismantled.) Bend them in a vise and hammer nice and square at the corners. Measure the exact distance, and make the bends marked at the vise edge-- It will be perfectly tight-- Holds the door closed equal to or better than then plastic latch..-- and slips on and off easily!
If you want a picture let me know-

Unfortunately, you can't get new spares. Your camera is an obsolete model and Sony (took over Konica Minolta) no longer support the model nor do they retain spare parts.

Your only option is to look on auction websites for a broken example, or to even ask on your local FreeCycle and Freegle groups. But if you do buy a spares donor make sure to ask whether the part you need is functional and present. After taking what you need you can try reselling what's left. I often find that by doing so I get virtually free spare parts.