Keep your gear up to date and melded. The greater the difference between your gear level and the recipe level, the harder it will be to get HQ. Use a CP/Control food to supplement your stats.

CP is important. The more CP you have, the more actions you can use that conserve/restore Durability to allow more Touch and Synthesis steps (not to mention be able to afford the Touch steps themselves). The Control bonus from Inner Quiet at higher stacks is a lot more effective than adding a little more control directly to your gear and having fewer Inner Quiet stacks because you ran out of CP.

Be careful when using Waste Not/Waste Not II. Using any action that does not have a Durability cost while they're active is wasting their effectiveness and part of the CP spent on them.
They're very good at higher levels when you're also using Groundwork/Preparatory Touch and still are useful at lower levels but you need to use caution with your timing.