Can a Bloodhunter Mutant consume Mutagens towards the end of a short rest?

I’m considering playing a Bloodhunter Order of the Mutant (Updated Version). Starting at 7th Level one gains the Reconstruction Mutagen:


Prerequisite: 7th level For 1 hour, at the start of each of your turns, you regain hit points equal to your proficiency bonus if you have at least 1 hit point, but no more than half of your hit points.

The Text of Mutagencraft reads as follows:

As a bonus action you can consume a single mutagen, and the effects and side effects last until you finish a short or long rest, unless otherwise specified.

Due to the 1 hour Duration of Reconstruction the effect would outlast the end of the short rest effectively pushing the number of active mutagens to 3.

Much later at Level 18 this becomes much more interesting due to Exalted Mutation

As a bonus action, you can choose one mutagen currently affecting you to flush from your system and end, then immediately have a mutagen you know the formula for take effect in its place.

Enableing you to switch the 1-hour duration mutagen to a long term one, at this point effectively enabling you to be under the effect of up to 5 long term mutagens at a time.

The Text of a short rest specifies the activities one might take during that rest:

A Short Rest is a period of downtime, at least 1 hour long, during which a character does nothing more strenuous than eating, drinking, reading, and tending to wounds.

Consuming a mutagen in my mind would count as drinking or eating something.

Am I missing something here? Is this possible? Would you allow for this in a game?