I had a lot of trouble with this too. Hell, I'm pretty sure I bought half of all the Pudding Flesh on Gilgamesh (5 or 6), but never got HQ. Luckily, someone was selling the HQ Mega-Potions of Vitality on the market for around 3,000 gil. I'm not sure if they knew its real value, or were just kind (they were selling two, after all), but I thank them all the same.

But I digress. There may possibly be two other instances where you can find Pudding Flesh in Thanalan:

There's a level 20 levequest for the Immortal Flames in Drybone where you have to fight a sorcerer that summons monsters. The last one he summons is a Moldy Pudding at 20% HP. If you can restart the fight by running away, then he may be able to summon the Pudding again. If that is the case, then you could feasibly farm four or so of the monsters.

In Little Ala-Mhigo, there's a levequest called "Necrologos: Fluid Corruption". You have to gather 4 pages from normal enemies, and they summon a Moldy Pudding.