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.

[![Blender Perspective Plotter Add-On][1]][1]

Here's a good video showing the camera [alignment process in Perspective Plotter][2].

>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).


  [1]: https://i.sstatic.net/7OzBb.png
  [2]: https://www.youtube.com/watch?v=4k8QReCNPNI