This is very much how I went about it, except that I actually put in the time reading textbook-like grammar resources off and on for years and never remembered any of it. Looking things up as I went along with reading material above my level allowed me to finally start to learn grammar.
Once I had the basics down, I found watching through one Cure Dolly grammar video each day really helped me make a lot of progress. Because I was already reading and figuring my way through grammar on my own in advance, I had at least been exposed to the material Cure Dolly covers, so it was easier to remember. And her explanations make a lot of things more clear than anything I had read about the grammar as I was reading manga and trying to figure it out.
We also have book clubs, in case you decide you want to plunge into the Absolute Beginner Book Club sometime, and learn even more grammar along the way in the discussion threads.
Good luck!