You're not going to like what I have to say. The man that installed your shower made a mistake a lot of installers do if they aren't familiar with installing shower drains. When I asked, " Are you saying that that the drain installation goes like this? Strainer, threaded drain flange lip that tightenes down on a rubber gasket?."
Not the correct way of installation. It goes like this. The threaded drain and lip, sealent, (plumbers putty) under the lip then underneith the shower pan the rubber washer, then the friction ring and finally the retaining nut that tightens the drain. That's the way we install them. To back up my claim I pulled up the installation procedure from a replacement drain.
Install the drain body down through the shower pan.
Don't forget to use the appropriate sealer.( plumbers putty)
From underneath, install the rubber gasket and the fiber friction washer, Secure the drain with the brass retaining nut.
You can see the entire procedure if you wish by clicking on; http://www.davke.com/installation.htm
To do the job the way it should have been done you will have to open up the ceiling and install the drain correctly.
Sorry to be the bearer of bad news. Tom