I have a 6.0 first of all....... but I was experiencing the same problem this winter. Slower and slower starts with 2-3 tries after cycling glow plugs to get the truck running.
Didn’t do any troubleshooting cause it was too cold here in the mitten but got lucky actually that the bendix (I think it’s called) finally went on the starter. It’s the motor that sends the sprocket on the starter to the flywheel. Anyhow I decided to replace the entire starter with a 6.4 unit and every single start issue was cured. Truck starts first try in -30 degrees zero Problems.
Back to you. Try putting a 6.4 starter on your 7.3. A google search shows that all 7.3,6.0,6.4,6.7 starters are compatible. This takes less than a half hour to do and I swear it will improve your situation. I was skeptic but words can not tell you how thankful I was that the guys here put me onto the 6.4 trick. The price tag sucks but buy a brand new starter and put it on. You won’t regret