While it is possible something is starting to seize, more than likely Bob and Glenn are right, the starter just isn't getting a good shot. You could even try a temporary setup where you jack it up, put some new, short battery cables on it and set the battery underneath the car and see how that goes. Make sure your ground cable (both in the temporary and permanent repair) goes right to the bolt that holds the starter in place. That way you will know you have a good ground.

I had a 351 engine in a drag car that took 2 12 volt batteries to crank. I thought it was because of the high compression and the fact the batteries were in the trunk. I found out later (when the motor blew) it was that the bearings were starting to seize and the motor was truly tight. Once it fired up it ran normally, just like yours, so there is that remote chance you do have something binding up inside...............but do the easy things first.

Don