So the current system in itself for HQing does not need to be scrapped imo. It needs tweaking, I mean I think most crafters here have crafted numerous +1 items mistakenly and even a few +2's. Whereas anytime you try and craft a specific HQ it tends to not work out how you want, even if you gathering every material at +3.
I have a suggestion for an additional enhancement system, that will work in addition to what we already have, not completely replace it. Lets look at an example with a popular item.
Crab Bow, we archers love our Crab Bows. Lets say you take a ton of time gathering HQ mats, synthesizing hundreds of sub components until you finally get all the items you want at the proper HQ. Only to... Fail HQing it. This happens constantly.
Now I understand the need to not FLOOD the market with these items so here is my suggestion.
Each Item has a small bar at the bottom in its description. We call this the HQ Evolution Bar. After an item has been crafted, you can then enhance its HQ rating further. How? Simple. The same craft job that can repair the item can use the same repair material to push that HQ Evolution bar towards a +1 Quality.
Similar to repair a crafter would sit down and then FUSE the repair material to the item in an enhancing way, not a repairing way. So if I were to Fuse the repair mat for crab bow to it successfully the progression bar would go up 1% towards HQ +1. One the HQ bar reaches 100% the item becomes a +1 quality item, the bar resets and you now move it towards +2 and eventually +3.
Now as I stated, fusing would not be 100% success. For instance I could make 5 fuse attempts that only resulted in a 2% push toward +1.
NQ mats would not enhance the item in anyway. The item being fused would always need to be an HQ mat to enhance. The enhancement would normally push it up by 1% and if your very very very very very lucky it could essentially crit pushing the HQ quality up by 3% max.
This allows players to make their weapons HQ even when a normal synth resulted in a NQ item. This keeps crafters in the mix of making these items better and keeps DOLs in demand as well.
I would also make it so that items enhanced in this manner become untradeable.