Hi Robert,
I think you have chosen a good approach to calculate the magnetic parameters. In general, that is exactly what AiiDA-Fleur WorkChains do (except alpha and beta parameters are set in order to rotate spins to another plane for spin-spiral calculations).
I have been testing MAE, spin-spiral and DMI calculations.
I did not check if MAE produces an accurate result, one should always be very careful choosing k-mesh, fermi smearing energy and other cut-offs. What do you call the 'theoretical result'? When you try to
reproduce it, do you use the same aforementioned input parameters?
DMI Force-theorem calculations failed for me as well, I think there is a bug in FLEUR. Some time ago I reported it here (cannot attach the link, issue number 617 on gitlab).
Unfortunately I can say nothing about Heisenberg force-theorem, I have never tested this.
Best,
Vasily