Glad to see you are up and running with midi.
Let's sort out what you are saying and maybe the solution to the chase problems will present itself.
As you have figured out, the FCB1010 allows you to set up 100 patches (10 banks with 10 patches each). [Although I use mine in "Direct Mode," but that's another story.] So you can send out up to 100 different note messages (one note per patch) on a selected midi channel.
I worry that some will be confused that when you say "I use the 9th & 10th patch/bank to trigger a blackout and a chase" some will think that it takes 20 patches to handle one black out scene and one chase. I think what you are saying is that in each of the 10 banks you use the 9th patch to trigger a black out scene, and the 10th patch to trigger a chase. That's handy because you are not operating in Direct Mode, but it forces you to use 20 (two patches in each bank) of your 100 available patches for those two function. [If you were using Direct Mode you would need to use only two of the patches for those functions.]
Take a look at the "MIDI CHANNEL SETTING" table on page 16 of your manual. With only 100 patches you cannot trigger all 127 options the DMX Operator give you - probably no big deal.
More important, notice that chases can be triggered via midi using notes 120 - 125.