You definitely can't give all the nutrients it need just with Big Bloom. It's an incredible supplement, but as you can see see from the NPK values that are just fractions, it just doesn't have high enough levels of Phosphorus (P) and Potassium (K) to support flowering. Big Bloom is more like a supplement with lots of organic goodies, not really a base "nutrient" like the other two parts of the trio.
Tiger Bloom is amazing stuff, and really effective at helping make buds, but like you said it's the one part of the trio that isn't organic as confirmed by FoxFarm (at least that was the case a few years ago when I contacted them about it).
If you are not going to use Tiger Bloom (and alway use that one at 1/2 strength or less, it's really powerful) you should find another option that's going to have significant P and K for the flowering stage. It's normally never recommended to mix nutrients but I think Big Bloom would interfere less with other nutrients since it's mild and uses ingredients that don't often interfere.
I personally had great results with the trio, and great flavor, so I do recommend it if you've been using them so far.
If you're looking for truly organic nutrients, a lot of people like the nutrients by
General Organics for cannabis. It's made by the same people as General Hydroponics. That's the organic nutrient system I'm most familiar with, but there's tons of other great ones too, so definitely make sure to check around! One of the growers on here (
Royal Nugs) recently made an organic nutrient "tea" by brewing some
composted soil with water, then used that to water his plants. You can't get much more natural than that!
