Here is a way to work on both at the same time and its not a exploit just smart business. You will need to have a fair amount of gold to start this.

1. Gather all you ingredients, make as many potions as you can out of them. Head to first Alchemy shop
2. Buy all ingredients they have for sale, this will boost the amount of gold they have(until you leave the cell then it resets) sell them all of the potions you made.
3. Go to there Alchemy table make as many potions as you can, sell them back to shop keeper and head to next shop.
4. Rince and repeat at every shop until done. I managed 2 speech lvl 79/80 and 5 alchemy 34-39.

while waiting for shops to reset inventory just gather more ingredients.