Not gonna lie, the gimmick of the blackout is actually kind of entertaining to me. I do think it would need to be reigned in some (as opposed to what some have suggested), but generally could be a funny little addition. So, for comparative sake:
Grog:
Drink 1: Minor Drunk Effect (slight stumble)
Drink 2: Full Drunk Effect (stumble, vision)
Drink 3+: Full Drunk and Vomit
Rum:
Drink 1: Full Drunk Effect
Drink 2: Full Drunk and Vomit
Drink 3: Blackout Drunk
With the "Blackout Drunk" you would see your pirate stumble and fall to the ground (same as if you get killed) and then the screen goes black for say 5-10 seconds. In that time the game moves your character to a random spot on the Ship or Island that you're currently on. You then go through the wake up animation again when the screen comes back and you're in the new spot.
This would in effect keep both similar, while still also having them feel pretty different from one another. You could also make the Rum be a silly Gold Sink even, having the Tavern be the place that you can purchase it from (and they can have cool dialogue about their local "house brews" of it to go with their spiffy barrels they have). Maybe apply a "Chest of 1000 Grogs" type of thing to the Crates of Rum where they have a set number (albeit smaller) of times it can refill a Tankard with the Rum, slowly lowering the value of the Crate as though it were Damaged (could even just apply the Damage effects as though the drunk pirates start breaking the bottles as they finish them off).
I feel like this would actually be pretty straightforward to implement and would just be cheeky fun. It doesn't color the new alcohol in a positive light, much like Grog, as it only really hinders you in actuality. It also basically would just be making use of things already in the game with just some minor tweaks to accommodate it, so the work is basically already done.