I have flown my quadplane about four times, three of them being autonomous transitions.
During forward transition the quadplane usually pitches up/down as it gains/loses, flies what appears normally, then repeats this about two more times before stabilizing.
Your pitching issue may be caused by your Q_ASSIST_SPEED setting of 21. Try lowering it considerably (to like 15) to get it out of the mix. The image below shows the throttle increases in blue after your speed drops below 21m/s.
You have extremely high levels of magnetic interference when you run the VTOL motors. You also have very high levels of vibration. You need to fix both before you fly again. You also need to set ARMING_CHECK to 1 and fix all of the pre-arm warnings instead of just disabling them.