Last I been told,
At server's end, it is not possible to target homunculus actors by EXP boost items. That specified call does not exist, perhaps, yet.
There's probably a work around for it. The past homunculus loyalty event shows that homun can be individually targeted. And clearly the refinement system smiths such as Enriched Hammer know if a kafra shop item (enriched ore) is in the player inventory or not. So, a workaround might be the player has to go to visit a certain NPC with the kafra shop item "Scooby Snack" in inventory. The player asks the NPC to help use the secret method to increase a pet's loyalty. If only one scooby snack is needed to provide loyalty, then this would be similar to the prior homun loyalty events only now you have a copy of enriched hammer renamed to "Loyalty Training NPC".
The loyalty training NPC complies, reserve locks the scooby snack, then has the player go thru the forced chat of whatever words ipsem nore facilitis etcetera, boosts the pet loyalty to be loyal similar to the homun loyalty event, and then deletes the reserved scooby snack out of the player inventory.
But as you said, there is no specific call to target set the homunculus actor to a specific EXP. It is done manually be GMs adjusting the record. But I think that that scooby snacks should be treated similarly to gym passes in that more than one is required. It makes sense that a less loyal homunculus or pet needs a greater number of scooby snacks. But this would mean the player has to buy enough scooby snacks ahead of time to bring the homun to loyal status in one shot. So if the player doesn't have enough scooby snacks, the loyalty training NPC would calculate by subtracting the current loyalty value from 911. Assuming that each scooby snack gives 100 points of loyalty, the NPC would then tell the player bring back X scooby snacks within 30 minutes and the quest timer would be set. Using the quest timer prevents the loophole case where the owner allows the pet loyalty to drop between the time of contacting the loyalty training NPC and when the homun is fed the recommended number of scooby snacks.