Preorder Aetherite earring - DPS only :(

[Bonbori]

The quests are too hard. I couldn't complete the level 53 quest on my culinarian until I reached level 55, and bought nearly a full set of item level 100 gear from the moogle tribe vendor. It should be possible to complete the HQ crafting job quests with the gear you got from previous quests without 30 attempts at making the items with full HQ mats and finally getting one to go through at 20%.
Now, I just just ignore these quests until I level up enough to do them.

Um... this is just objectively, mathematically untrue.

You can usually guarantee 100% HQ chance of any craft required by your job quests even without melded HQ gear, but if you are struggling, it might help a little to craft a few pieces of level-appropriate HQ gear and meld some materia onto it. Materia IVs or even IIIs can be melded and pulled out with 100% chance so you can reuse them throughout your whole HW level range and even into early levels of Stormblood. On top of that, a full set of HQ materials literally does half the work for you. All Quality gains past that have increasing returns so quality points translate to increasingly higher percentages. But that shouldn't matter much because filling the remaining half takes very little effort, especially past level 50 when you have a huge variety of cross-class abilities at your disposal.
For example, have you tried doing Inner Quiet + Comfort Zone + Steady Hand II + Hasty Touch spam + Byregot's Brow/Miracle? It's relatively efficient and CP-cheap until you unlock Prudent Touch at 66, at which point you marry Prudent Touch and live happily ever after.

If the best you can get despite using HQ materials is 20%, you may be doing something wrong, or you may be slightly undergeared for your level. If it's the former, and you do not quite understand what to do, I recommend trying out this little utility. Provide it with your stats, tell it what you intend to craft and it will come up with a... usually somewhat reliable sequence that you can reproduce in your game step by step and maybe pick up a few tricks.