a 120 bag should help tremendously but it's definitely doable with the 4 bags you're using. I always get some contaminant in my 120 bag, mainly capitate stalks(the trichome stalks).
Experiment with different stir times but I generally keep my stirs under 5 minutes. And very gentle with a wooden spoon. The trichome heads should break off very easily. You'd be amazed at what a 2 minute stir can do.
And when I say gentle I mean gentle. Just like poke the wooden spoon in, shift it around a couple times gently and then a little circular stir, and repeat for a few minutes.
And a pressurized spray bottle helps big time to increase the purity. Matt Rize style.
You are right, practice makes perfect. Keep trying and you'll get there!