That Taco pump should work fine. Use the set-point mode and install the temperature sensor down stream from the closely spaced Ts. The pump's speed will vary to maintain the target temperature at that point. I've never had short-cycling with the set point modes.
I noticed that there appears to be a swing check valve located between the closely-spaced Ts.
View attachment 263913
That will need to be removed because there can be conditions where the flow rate from the storage tank exceeds the flow rate of the heating zones. At such times the excess flow from storage will need to flow to the right directly from supply to return. To do that the check valve should be removed.