Phase measurement and correction in IoTaWatt

As far a I know, that’s how everyone does it.

Those few words there demonstrate your misunderstanding of this. You can’t swap between a PF of 0.89 and a measurement of degrees (except in a spreadsheet or a textbook where pure sinewaves rule). Unless your heat pump is extremely old, I bet it has an inverter in it. It’s current signature is going to look a lot more like that of switch mode power supply, probably like the DC brushless motor in my washing machine. Here’s how it looks on it’s spin cycle:

My monitor clocked that signal at:

Apparent Power: 559VA, Real Power: 395W, Reactive Power: +115 VAR, Distortion Power: 378 VAR.

arccos(395/559) is 45 degrees, but that’s a completely meaningless quantity in this situation.

Did you read and understand: Measuring reactive power to build NILM system - #7 by dBC ?