Moral of the story........ become an Omni crafter if you want to reliably make HQ items.... lulz (a discussion for another thread). But yea like they said at MINIMUM you NEEED hasty touch absolutely neeeeed!! So level Cul to at least 15. All the other skills mention are OP in terms of up'ing your reliable HQ rates but you can actually still HQ without them.
If you have Hasty touch, you get a specialist version of every other skill that are necessary, although is heavily gated by RNG.
-you get satisfactions (SPC) instead of Trick of the trade(ALC) (trade is MUUUUUUCH better, but satisfaction is something )
you get By. Miracle (SPC) which is an OKAY skill compared to By. Blessing(CRP) (a difference of 100% potency at max IQ...very noticeable but again u could function)
Innovative touch (SPC) is actually better than Innovation(GSM), yes there is range involved which makes it less reliable but if it procs, it becomes more efficient usage of the buff and it has less cp required.
Trained Hand(SPC) is a very gimmicky skill and it doesnt really cover any omni skill directly but again its efficient if the stars align (read the tooltip for details)
Nym. Wheel(SPC) is actually the best POTENTIAL durability/cp managment skill but again its gated by RNG and you're already a LTW so you have the Waste not's
Whistle while you work helps with progression since u don't have Muscle memory (CUL) or Maker's Mark(GSM) or Piece by piece & Rapid synth (ARM)
You have no specialist skill that covers Careful syn. II (WVR 120% progression at 100% success rate for 0 cp.... is just really really an OP move)
And really this is all you need if you want to be able to make HQ SOMEWHAT reliably especially if you add in Delineations (more RNG and more work to get them but overall a plus in terms of hq rates).
Moral of the story.... if you want HQ become an Omni...... or if you want HQ and don't mind more RNG than omni's experience then just get Hasty touch from cul and use your specialist abilities, its do-able (I personally wouldn't say fun....but doable ).