Starter circuit diagnosis for blown fuse

My 2006 Miata failed to start yesterday when I tried to fire it up for my third autocross run of the day (15 minutes after prior run). I turned the key and it cranked for a partial engine rotation and then stopped. Lights worked and everything else seemed normal so a couple of grid workers gave me a short push and it started easily.

After the third run was group 2 runs and a break for lunch so I tracked down the issue during lunch and found the 20 amp starter circuit (ST) fuse had blown. I stole the 20 amp defrost fuse and it fired up (1.5 hours later). I then started it for run 4 with no issue (2 hours after prior run). I went to start it for run five and sure enough the fuse popped again (15 minutes after prior run). After another push start I completed run 5 and let it idle so I would not need another push for run 6. I shut it down after the final run and stole the 20 amp wiper fuse which started it for my drive home after group 2 runs, course clean up and awards (2 hours later).  

With a cold engine this morning, I started it 10 consecutive times with the standard 20 amp fuse. Later I will go out and try to get it hot and try some consecutive starts to see what happens.

I assume this circuit provides power to the starter solenoid. The Miata forums generally indicate "bad starter" but I am leaning towards a solenoid that is starting to fail. Mazda does not sell a "new" starter, only remanufactured units. They do sell a new solenoid. 

it is apparently a pain in the rear to swap the starter due to limited room so if I mess with it I of course would prefer to only do it once. 

I think the heat/underhood temps are a factor but not 100% confident on that yet.

Any other testing that you would do before deciding on a course of action? What course of action would you lean towards based on the information presented? 

No specific knowledge of an NC, but I would verify that you have good continuity between the engine block (preferably from the starter body to then battery ground.  Then do the same for your positive wires running to the starter.  Then try it hot.  In an autocross setting, you generate a lot of heat quickly, then let the car sit and really heat soak everything..

Resistance raises with heat, so if this is only a problem with hot, make sure you eliminate the possibly that your engine ground straps didn't corrode away..

Edit: sorry, bumped post.

That said, solenoids don't pull a ton of amperage, and that's all the fuse is protecting, so it is very likely that the solenoid is jammed up a bit or corroded and drawing excessive amperage.   You should be able to verify with an ammeter if you have one.