Every HQ above 45 I got was either from HQ mats or Hasty touch with Steady hand II.
Granted I don't have Ingenuity II either and I have a feeling you might be better off using a lesser tool for recipes of Ingenuity II.

I don't know if that skill reduces the recipe to 47 or 52, based on the tool you have in. (ilevel 55 tool)

If it's flagging the recipe based on tool, you could use a level 48 tool and actually lower the recipe of your synth to 45 and you might find that works better.