I also loved my MaMa Carefulsynth for two star over Rath's approach because of the additional "wiggle" in the progress. You have to be more aware of not falling short or early completion with Rath's. With this said this also meant you can sometimes squeeze out two extra ToTs during the FS cycle in Rath's approach (and this is very common in three star crafting).

As for your questions I generally approach as follows with the modified Rath's rotation at max CP. I push to get two ToTs during the FS cycle. I keep in mind this sometimes leaves me short progress and make sure to do one extra careful synth when needed. During the rotation I push for 1 or two precise touches. So by the end of the rotation I typically have two 18 CP actions. If I ToTed twice I also have 4 extra CP (which I use to convert the final SH to SHII). So my final sequence is usually SHII, Hasty, Ingenuity, Basic Touch, Greater Strides, Byregot's. I do this if I have 8 or more stacks OR 6 or less stacks going into the final rotation. If I have 8 or more I'm going to max out if I miss the last hasty or not and I'm fairly certain I get somewhat more quality using the innovate on the last two actions. If I have 7 stacks two basic touches is generally better as I believe 9 stacks+ is the ideal breakpoint usually (unless you have 0 starting quality). If for some terrible reason I have 6 or less stacks, that innovation is much needed to squeeze out as much quality as possible.