Thanks everybody for your help.
I'm going to do as Momma.of.two suggested and add spines to the top and bottom, and secure the corners of the dividers. I think I'll use superglue there (not too keen on silicone after all the scraping I just did), I'll just be very careful not to make a mess, maybe brush it on with a cheap dollar store paintbrush I have hanging around.
On another site, someone had then put a single strip of black tape down the front of their tank after this kind of divider was in place and I'm going to do that. It hides the glue and spine and blends with the plastic frame.
I'm also going to find a couple rocks and put one on each side of the canvas for extra support.
Cody, I still appreciate the suggestion, even if it doesn't work for me because I'm going to stock small species, it might work for someone else.