Results so far:
Something like 6 hours at room temp and only the barest suggestion of a tint using heavy concentration of navy blue all purpose liquid Rit dye. You have to put the part side by side with cutoff material from the bottle to convince yourself there is any tint at all.
Next try was an hour or so at maybe 120F-140F. This left a tiny bit of tint. Not much, but enough to take away the stark clear look. Might try to go hotter, but don't want to melt the baggie holding my dye. Will have to test the bag (without the dye) in a hotter pot. The tint at this point does not seem to be affected by cleaning with Windex.
After going thru Rit's website, I see that they now have a product called DyeMore. It is intended for synthetic fabrics, including polyester, which makes it sound promising. They also say that to dye these fabrics, you need to achieve "...an almost boiling temperature..." of the dye bath. That perhaps explains why I didn't really get any tint until I heated the dye a bit. But I also do not have the newer dye they recommend for synthetics.
In comparison, an acetate canopy would be nearly opaque by now. (I did that to an Aquila canopy years ago, thinking it was going to be hard to dye. It wasn't.)
So next I will get ready to "almost boil it" using scraps. If that works, then I'll do the canopy.
If I was serious about a dark tint, I'd definitely go buy the synthetic DyeMore variety. They have a bunch of great colors that would likely look good on a canopy. It costs about $6 around here. Since I am rebuilding/completing an OPP, this material is not worth the $6 and trip in the pouring rain to me.
If the heated dye bath doesn't help any, I may dump some vinegar into the mix, as Larry suggests. Not sure what kind of alchemy he is getting me mixed up with. I will draw the line somewhere after the eye of newt and tail of lizard.
Divot
https://www.ritdye.com/products/sapphire-blue/