Problem is that at low speed, with the heat pump in circuit, there is not enough pressure/head to operate the water feature or the chlorinator.
Actually, your problem is just the opposite. You have too much pressure/head which is reducing your flow rate. I think you meant that you want more flow rate not pressure.

There is clearly an object(s) that is causing fairly high head loss. When you bypass both the heater and the filter, the pressure is still pretty high. Plus the pressure is high when backwashing. It just could be you have a lot of high head loss components.

I would not want to guess at a two speed pump size because right now there are too many unknowns. A VS would allow you use trial and error to hone in on the appropriate RPM and flow rate to minimize energy costs.