Any tips for my cooling problem

Hello guys!

Recently I've got my first Gixxer, a 750 K4. When I first got it I flushed the cooling system and refilled it with 100% antifreeze. I've bled the system at the radiator inlet port and it's been functioning well for 3 weeks.

Yesterday was a rather hot day and when I came home from a long ride and put the bike away the temp was showing 106C/222F and I could hear boiling sounds. The bike spit out fluid from the expansion tank overflow. The fan is working correctly and coming on around 104C/220F. Usually the bike cools down quickly when I ride, but yesterday at the end of the ride it was constantly around 104C/220F, even in cool air with +50Km/h.

Now I bought a manual after I did the flush and found out Suzuki wants me to mix 50% antifreeze and 50% distilled water (and not 100% antifreeze). Also I found out you can bleed the system with the bolt on the thermostat's cover.

I wanna diagnose why my bike was boiling and overflowing coolant, but I was hoping you guys have some tips for me. I don't have the equipment to do a pressure test on the radiator-cap or a thermometer to check the thermostat. So I've bought those parts new and they should arrive tomorrow.

Is it okay to proceed like this, or should I do it differently:
1. Drain current (100% antifreeze) coolant
2. Replace thermostat with the new one I ordered
3. Fill system with 50% antifreeze and 50% distilled water
4. Start it up and diagnose if the water pump is working well (I don't know how i can diagnose this, any tips?)
5. Bleed it at the radiator inlet completely
6. Bleed it at the bleed bolt on the thermostat cover
7. Install new radiator cap and expansion tank
8. fill expansion tank
9. clean out the radiator and straighten bent fins

All tips are welcome, thanks!