It can still happen with a lower chance of HQ. I personally leveled BTN to 32 to gather Flax around Camp Tranquill. For Linen Hat, I used to mix 2 HQ with 1 NQ like you did (HQ undyed linen and HQ linen yarn or 2 HQ undyed linen with NQ linen yarn) and managed around 90% HQ I think. BTN is really just so you don't have to buy the HQ Flax. I think I got about 1 HQ to every 2 NQ. Speaking of which, I thought Linen yarn required 3 Flax lol. Did they change up the recipe? Once I got Byregot's Blessing, it became a whole lot easier to HQ stuffs.