Double check that the starter is perfectly flat against the bell housing. Could be the starter drive hanging/binding on the flywheel.
Pull the starter wire from the relay and have someone check the starter side of the relay with a test light while you crank it. If the light stays on after you quit cranking then the your ignition switch, relay or bad wiring is giving the starter power for too long.
If none of that works than probably something wrong with the bendix drive in the starter getting stuck, or you somehow have the wrong tooth combination between flywheel/starter.
The starting system is pretty simple. You got the switch, a solenoid, and the starter. The solenoid is cheap enough to just replace, the switch and the starter you can test.
I know you said its not your flywheel because you just replaced it....but.....everything on my car works perfect until I decide to mess with it.
In other words, if you never had a starter problem, changed your flywheel, and all of the sudden continue to have starter problems, only one thing has changed in this equation, and thats the flywheel. Something to doublecheck you did right. Did you get the right flywheel? Is that the original engine in the car? Make sure you ordered the right flywheel weight, tooth count, and starter for the engine.
Also, if you changed your flywheel, that means you had the large shield in between the bellhousing and engine out. Make sure you put it back in. If you dont, it can throw the clearances off and cause you problems. Of course, I have seen some people run it without and do just fine, others have problems. (someone else mentioned this above I believe.)