Zone 1: The first is an electric-powered heating/air unit (forced hot air) that heats/cools the first 2 floors of the home. This system is located in semi-conditioned space on Floor1.
Zone 2: The second system is a heat pump that controls the temperature on the 3rd and 4th floors. This system is located in conditioned space on Floor 4.
Find out a bit more about the Zone 1 system if you can - if it's a heat pump, great. If it's just resistive coils ("electric furnace"), it's going to be painfully expensive to run. Heat pumps are significantly more efficient.
It has recently come to my attention that I may have had the settings programmed so that the two zones/systems are actually competing against each other.
Unless one of them is actually switching to air conditioning, there's no way they'll "compete" - the options, in heating mode, are "heat" or "don't heat." Competing against each other would be, "One is heating, one is cooling."
So I’ve been experimenting, and measuring temps at different times of the day, and what I’ve realized is that Zone2 rarely puts out “Warm” (>70 degree F) air (although sometimes it puts out 85degree, so I know it’s not broken). It also seems to run a lot more than the Zone1 heater.
The "slightly warmer than ambient" air is how heat pumps work. When the higher temperature is coming out, it's likely using the backup coils, which are really expensive (they're just big resistors, like your first story heater).
Goal : At 6am, I would like a warmish bed/bathroom on Floor3.
A small electric oil filled heater in the bathroom will probably be easier here...
So 67 will eventually heat the upstairs, but it sure feels cold on my shoulders in the morning!
Heat it before you wake up and turn it off when you get out of bed.
Is there an order in which I should try to heat the house so that the heat pump doesn’t have to work as hard and so that the air actually feels warm as it’s coming out of the vents?
You want to use the heat pump whenever you can, in terms of heating cost - they're radically more efficient than an electric furnace. They just won't get "hot" air out of the vents unless you switch the backup coils on. I suppose if you didn't care about cost and wanted warm air, you could run the heat pump with the backup coils (details of how to do this are up to your thermostat) and get quite warm air coming out.
I've been told that with a heat pump, it doesn't make sense to let the temp drop well below normal as that causes the electric emergency heat to come on and basically negates the benefits of having a heat pump.
That's true because the default thermostats installed with heat pumps are stupid. If they see more than a few degree difference between "set" and "actual," they'll panic, turn the backup coils on, and try to make the difference up as quickly as possible. This is idiotic from a cost of heating perspective.
If you have a not-stupid thermostat, you can tell it when you want things warmed up and it'll do what it can with the heat pump before using the backup coils. I have a Nest, and it will often start heating at 4AM to have things up to the desired temperature by 7AM. On a warmer night, it'll start later. It uses the emergency coils on occasion, but not terribly regularly, and I'm reasonably certain it will have paid for itself with electricity savings this winter.