If the transaction is correct, and the statement "Basically, in order to synthesize an HQ final item, HQ versions of every ingredient must be used. " meaning that we are not possible to made HQ item if we don't have all HQ ingredient, then I think SE is TOTALLY IN WRONG WAY! This sound like all or nothing design, but which successful game will have such design? The most interest thing for me in the game is the uncertainty. For course, the random factor should never affect too much, but a little bit uncertainty will make the game more playable.
For me, the best modify way is to reduce the random factor in current synthesis. In my experience, I've got HQ when I make the Apple Juice at CUL34 with quality <30, almost got 1 HQ+1 for every 30 times. But when I try to make black pearl in CUL35, and each try got 200+ quality, I only got 2 HQ+1 for every 30 times. WTH! Synthesis of black pearl is 20 rank lower than Apple juice, and quality of each black pearl synthesis is 5 times of apple juice!
SE, you should blame of the random factor! I can't see linkage between quality and HQ. For the same synthesis at the same rank, I always find that i would get HQ with normal ingredient but NQ product with HQ ingredients!
For my opinion, it would be better if quality actually link to the HQ rate, and ingredient link to the quality:
0% HQ ingredient -> start with 0 quality
10% HQ ingredient -> start with 50 quality
20% HQ ingredient -> start with 100 quality
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100% HQ ingredient -> start with 500 quality
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500+ quality -> 100% HQ product
450+ quality -> 95% HQ product
400+ quality -> 90% HQ product
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0 quality -> 0% HQ product
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In this way, low rank crafter would make HQ product by using more HQ ingredient, experienced crafter or high rank crafter would use less HQ ingredient. If a crafter have correct point assignment, with master support, apple juice or other food stuffs, full moon phase, then it would be easy to make 200+ quality for same rank synthesis.
This design favor high rank crafter? yes, why not? i am not bot, i paid all my gil in crafting, i even sold my 50nm item for gil to buy crafting materials, i pay more time in rank up my crafting rank then battle rank, so why i can't make HQ product easier? People should get more if they pay more in this area, why this should not be true?