NEWB: Getting rid of Lilac, going Titanium. HELP

*ott*

8 weeks ago i went from bright red with the front blonde, to black all over and lilac in the front. the red wasnt covered as well as i had hoped after a few washings, but im sure after this round of dye i should have a more even color.... and the lilac faded to a funky color. i'm hoping to turn the lilac section into titanium, and therefore I am looking for ways to get the lilac out. The current picture isn't great, but the color is grey, although a girl in one of my classes said it looked green to her. *shrug* I'm new to doing different colors myself but figured it was a skill that would save me money in the long run.

How do i remove the last of the purple?

I've tried washing with dish soap, leaving on coconut oil, and leaving on shaving cream.

red and blonde:
https://www.facebook.com/photo.php?fbid=1053834244626814&l=2423e05f5b

black and lilac: (i used a purple toning conditioner to get yellow out prior to using lilac)
https://www.facebook.com/photo.php?fbid=1096497487027156&set=t.100000007457958&type=3&theater

Current:
https://www.facebook.com/photo.php?fbid=1053834244626814&l=2423e05f5b