i don't really think it is appropriate to refer to "phasing in" an organic program, unless you're working like an ant on your lawns.
1. if you're using chemicals, you are harming the delicate ecosystem in the rhizoshpere, which isn't just NOT an organic program, it's actually working AGAINST an organic program. so i assume when people talk about "phasing in" or "half-and-half" programs, they basically mean building up SOM. if that's what you're doing, that's not really an organics program, that's just adding compost apps to a chemical program--granted, you may be reducing inputs of chemicals, but it's still just compost.
2. if you're fixing up the soil after chemical apps with additional tea apps or whatever you might do, then i suppose this could be a true mixed approach to lawn care, blending organics and chemicals. but frankly, this seems crazy to me. you're basically doing twice the work than you ought to. you add a chemical, then you come back shortly after to regenerate the activity in the rhizoshpere. i thought that the main barrier to doing a balls-to-the-wall approach to organics was cost. it costs a lot more money, time, expertise to turn a lawn off chemicals and minimize the struggle your lawn is in to stay beautiful while SOM is low and the soil food web is inadequate. but if you're spending all this extra time to cancel out the damage your chemicals are doing, you might as well just put that cost into more organics activity.
i guess there are ways to phase in organics while still keeping chemical practices going, i just generally think people aren't truly doing that. and i'm not even arguing whether the phasing-in approach or the all-out approach is better. i just want you to consider that you are either still chemical (+ one additional service) or you might as well just go all-out organic for the time and cost that you need to put in to a serious half-and-half approach.