There's a few scenarios that can occur to allow you to kill Gut discreetly:
1) Get put to sleep by her potion and have your party pick the locks (Or steal her key beforehand) to go into her basement while she's still talking to your character. Of course, this won't work for Elf/Half-elf which are immune to being put to sleep (But you can have one of your non-Elven companions talk to her instead).
2) Antagonise her and try and beat her in 1 turn before she calls for help.
3) Attack her with your whole party while she's in her room alone and beat her in 1 turn before she calls for help.
4) Attack and kill her and simply run into her basement before someone bangs the drums which will de-escalate the situation (As the other goblins will only be "Temporarily Hostile" from being called which can be cleared by leaving the area)
I find the easiest way to beat her on the down low, is bring my entire party in the room and then spam Hold Person on her until it lands (She has pretty high WIS saves being a Priestess and all) since for whatever reason, that spell doesn't cause aggression even on Tactician. Once it lands, go to Turn Based and have your party wail on her with 100% accurate critical melee attacks.
I drank the thing and nothing happened and suddenly she aggro's me. Surely a priestess of her stature would know I was a HE and would know that sleeping potions wouldn't work on me...
You say that but, goblins - Even Priestesses - Aren't the brightest crayons in the box. Also, outside of the recent takeover by the Absolute, they won't have had much contact with other races besides killing and/or eating them what with their limited social tendencies.
Like, the most well read goblin you can encounter is found reading one of Volo's books which is not the most... Accurate of sources.