Sanity check on replacing flow check valves

I have a 3 zone system and want to replace all the flow check valves since I'm having issues when the 2nd floor is calling for heat, the hot water also flows into 1st floor even though its not calling heat so on and so forth. I haven't done this before but I have a plan written and would love your thoughts: My setup: Flow check valves: 1. Switch off power to the boiler 2. Turn off gas to the boiler 3. Close off water supply going to boiler 4. I'm assuming I need to drain the entire boiler to change the flow check valves. Can I simply just drain everything from that one valve on the bottom of those pumps or would I need to drain each individual zone according to the picture?: 5. Replace all flow check valves 6. Turn water supply back on 7. Re-light gas pilot 8. Bleed the system 9. Turn power back on boiler