Three and Two Stone Fuseki
Imagist: I have tried this opening as white in two-stone handicap games a number of times, creating the "Chinese enclosure" with my first two stones. Normally in two stone handicaps, two corners are taken and then white gets the first kakari, but this encourages black to attack first. I can generally make black's life miserable if they invade, so this has good results for me. However, I consistently lose when black completes a sanrensei formation along one of the sides instead of attacking.
Imagist: I have a personal preference against the mini-Chinese because seems inconsistent to me. and focus on rapid large-scale development, and in that respect, seems better placed farther from white's other stones. The framework of and also provokes an invasion at one of the a points, with the intent of creating a weak group, but the introduction of allows black a good attack at b which will either weaken the / framework preparing for an attack at a, or make seem misplaced (white cannot attack the b invasion from both sides simultaneously). Lastly, all of white's stones are on the third line, and white cannot afford to play so low with black starting out so far ahead.
That said, I'm presently 16k KGS and 11k AGA, and much stronger players have good things to say about this strategy, so one shouldn't hold my analysis in very high regard.
Bill: You have had good results when Black invaded between and . But after is a dual purpose play that makes territory while threatening an invasion. It is unpalatable for White to go back and protect, particularly when giving two stones.
Imagist: In my opinion three stone handicap games should be on a different page, because in two stone handicap games, white gets the first chance to attack, while in three stone handicap games, black gets the first attack, which makes the basic opening strategies completely different. Here is the best strategy I have come up with for this situation. While does not entirely ignore black's approach, it develops white's position on a larger scale than any joseki with which I am familiar. The most common response I see from this is a second kakari at a, which is loses some of its effectiveness because of . The other approach I see is the invasion at b, which allows white to create a nice upward-facing wall. Whatever happens in the corner, white is now well-prepared to kakari at c, making a dual-purpose move (aiding the lower corner and aiming at the upper corner).
Bill: Let me congratulate you with coming up with the idea of . It is unusual, but certainly playable.