I did some thorough testing. Imo it's impossible to craft superb weapon in Dawnshore because there is not enough paradisan ladder and this material as same as adra doesn't restock if player buy it from vendors. I tried to savescum gathering paradisan ladder with scavenger perk (scavenger 2 is required to optimal crafting), but the quantity seems to be predetermined. Some will always give 2 pieces and other 2 + 1, no matter how many times I reload the game. I restrained to picking up herbs until I get scavenger 1 perk.
Optimal path is to buy fine one-handed weapon (it's critical because two-handed weapons require more materials), upgrade it to fine +3/3, use 9 adra gathered in Dawnshore to craft 3 pieces of awakened adra, then upgrade this weapon to exceptional quality. I recommend not spending paradisan ladder for upgrading armor to fine quality. During the quest with luminous adra it's best to side with captain Trevik and kill captain Bardatto to get fine breastplate from her corpse. Then it's time to gather all unique items. They will provide at least 8 awakened adra pieces and the ninth can be just bought in form of exceptionall item from any vendor - beware that Sanza and one of twin sisters have fixed quality of unique items determined in the moment you first time look at their stock.
I did 3 speedruns of Dawnshore content. There is some inconsistence. For example killing Octav without checking his loot and going back for it with exceptional weapon sometimes spawn his weapon as exceptional, sometimes in lower quality - but I'm sure I didn't cause game to display tooltip, so it's weird. Sargamis is the same - sometimes I came back for Last Light of Day and it was exceptionall 2 times and one time it ended as fine weapon - even without triggering game to displaying the tooltip. Quality seems to be tied to the weapon you used while killing him.
All unique items in chest have their quality determined if you are close enough to point at the chest to prompt "open" interaction. Even if you won't open the chest, the game will set its quality. It's best to avoid two chests with unique armors like Arcanist's Gambeson and Stelgaer's Pride until you kill captain Bardatto.
@Lonion wrote that it's better to use common weapon as upgrading template. I disagree. Sure it doesn't require adra, but adra isn't an issue in Dawnshore. You can get enough even for superb upgrade. Paradisan ladder is the issue and common weapon needs gold and more paradisan ladder for quality upgrade.
Nevertheless three times in a row I leaved Dawnshore with Exceptional +2/3 weapon with enough adra to craft 3 Corrupted Adra and missing maybe 5 paradisan ladder to upgrade my weapon to Exceptional +3/3 and then immediately to superb. Main crafting materials like branches and metal chunks can be bought from vendor because these are restocted. I crafted superb weapon in the starting point of Emerald Stairs, after bringing Yatzli the vase and setting up first camp in the region. Since then all unique weapons scale to superb (IV +0/3).
If you won't exploit this system but still pick scavenger perk you should finished Dawnshore with at least exceptional +0/3 weapon (even two-handed) and fine armor.