Hi, I have Project Magenta and Airbus full setup. I used to have same kind of up and down pitch behavior during climb. Past years I have noticed that the model you use and some parameters will affect autopilot. There is manual but quite limited info about what values and how they affect considering ini of cfg files. Also support is pretty random as far as I have experienced.
Do you use exactly recommended aircraft model and FMC type file from PM update page? Newest builds?
In P3d you have aircraft folder that includes your preferred 737 aircraft. There is aircraft.cfg file. What do you have in those lines : aileron and elevator effectiveness? What about pitch stability setting? What is you Thrust scalar value?
I know nothing about PM737 software, but Airbus has possibility to use either FCU autopilot parameters to control pitch and bank or special PmFBW (fly-by-wire) software. I use FBW because it has more sophisticated control options over autopilot.
Yours, Markus