+1 on that ^

I think scenario 2 is unrelated to your normal issue and you might have mutiple issues happening.

Have you ever tried boosting (cables I mean. turning up the boost on a in-op car has proven to give poor results) it when hot and it doesn't turn over? If you tried this, without the roll bump manoeuvre first, and it went you could narrow it to battery and or starter. With cable and a jump it might give a bit of a push to a weak starter or battery.

Also you could try checking your battery voltage before your first cold start and then with the car running. Maybe the alternator is not giving a good charge.

Just my two cents and a couple of freebies.

This link won't be helpful but might make you feel better.

Try it now