Instead of fSpy or BLAM you could also use the relatively new Perspective Plotter commercial add-on: https://blendermarket.com/products/perspective-plotter
This will save you to hop between software for the calibration step which makes re-calibration a breeze.
Here's a good video showing the camera alignment process in Perspective Plotter.
Disclaimer: I'm not in any way connected to the add-on producer. I'm merely a user of it and didn't test it for projection mapping (yet).
