ajspiano,
I got a chance to watch your video last night, thanks for posting that! In one part you said you wondered why I say "snap" instead of just "play." Well, I think the reason is that....during an improvisation, I don't really know when exactly I'm going to be describing a third or a sixth. That particular vertical harmony might be displaced in time because of broken rhythm for instance. "snapping" is sort of a vague goal. It doesn't even mean play both tones of the third or sixth at the same time. It just means that it "attracts" simultaneous voices. The exercises you've devised for yourself I'm certain will be just as effective. I can't imagine there's any "wrong" way to approach this.
However, as Ted points out probably the hardest thing to really communicate when discussing improvisation is exactly *how* something new can come out. Baroque presents an interesting challenge in that patterns can easily become locked in physical memory and be hard to break out of (you touched on this in your video ajspiano).
It's possible the simple answer is just to continue to inject randomness amongst order. When I started out as an improviser, the only real "order" I had was knowing some scales and chords. Beyond that, it was almost all "injection of randomness" that led to the experience required to create something musical and interesting on the spot. With baroque improvisation, I've sort of come full circle. I had to create some order (fixed anchor voices or patterns or whatever else), and then inject randomness. It's still a challenge: On some days I'll feel hopeless and just be locked in these well known patterns. On other days, it feels far more malleable and I'm able to break up the rhythm and timing enough to make the familiar patterns sound new. To me, that's essentially what Bach's art was all about. He uses the same patterns and devices all over the place, but each piece is unique and interesting because of broken up melodic and rhythmic timing and displacement of multiple voices.
*edit* To add an idea to the above paragraph---one thing I've sort of learned in recent playing is, with baroque improvisation we are not locked into a time signature. As you begin playing, even in the first few notes---you don't yet know if you're playing with groups of 4, or 3, or 6, or 8, or 12 etc. etc. So you can literally do almost anything you could imagine, land on any dissonance you can imagine---but if you keep that vague goal in mind of hearing thirds and sixths----you may find with experience and practice with spontaneous play that something new will come out and an arrangement of thirds and sixths will be described (more or less) in a new displacement in time that you hadn't yet thought of before. Not sure if that makes sense.
To put it another way--when we practice fixed patterns, or fixed scales, or fixed anything---the temptation is to NOT break it up. But if we practice taking a leap and messing with the rhythm more than we thought should be possible--it can create startling surprises. I think of several spots in Bach's sinfonias I've been playing recently where in the middle of the phrase there's some very ugly dissonance but soon there's another full harmony. As an improviser---it doesn't matter when this happens. All the ear hears is a succession of full harmonies---some time. It does not count 123412341234 or 123123123. What I'm attempting to communicate is that---once one gains enough experience, baroque, paradoxically, will seem and feel just as free as any other improv style. Sounds crazy?