The simulator has a bug for Ingenuity and isn't accurate. But you can safely switch to ingenuity I as follows:

So somewhere inbetween 790 and 800 craftsmanship (with your foodbuff included)... you could in theory use the Extra Progress rotations with Ingenuity I. With 419 base CP this would give you two free Precise/Basic (or one free precise and innovate). This would further improve the overall HQ chance nicely, effectively reducing your need to hit another hasty touch.

So in theory:
MaMa Careful Synth (Max CP, Extra Progress, Ingenuity I, Requires 10/13 Flawless Synth) Required stats 790-800 Craftsman and 467 CP
MaMa Careful Synth (Max CP, Extra Progress, Ingenuity I, Requires 9/13 Flawless Synth) Required stats 820-830 Craftsman and 467 CP

WARNING THOUGH I need to actually test this theory to see what the craftsman breakpoint actually is. I'll test this out on my blacksmith and weaver this week. I can equip the Blacksmith to be over 830 and Weaver around 790 to test this theory.
* One problem with this theory is you would actually need 421 base since 8+8 is 16 not 18... or you could use HQ Seafood... though a single ToT proc is 20 CP... so one ToT would also put you even. Max equipment CP is 422... so any way you cut it we're getting fairly high end with the rotation theory here. I personally sit at 420 (with +3 CP in main/offhand rather than +4)

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As you noted you could use this approach to lower your CP threshold and do the synth with less CP or add another touch as I noted.