Also note that your statement says that there exists a good filtration with some property not that every good filtration has that property.

I think you are mistaken that your filtration is good. You want something like $M_n=D_n.(1+D_\mathbb{C}P)$ where $D_n$ denotes the differential operators of order at most $n$. You will only get $M_n=M$ for some $n$ if $M$ is an integrable connection ie a f.g. $O_X$-module.