To add
Did some testing today at GCTS. It seems that the plane struggles to keep with the vertical guidence of the ILS. It will drop below and try to climb back, but then go far and nose dive etc etc. We get this oscilation and for me its starting around 5nm from the runway. Seems it was this oscilation that caused me to nose dive at the runway originally.
This was all on A/P with A/T - I made no input just so I can see how it behaves.