RAW, this works.
A strict rules as written ruling here is easy enough. A short rest allows you to regain hit points at the end of a short rest:
A character can spend one or more Hit Dice at the end of a short rest, up to the character’s maximum number of Hit Dice, which is equal to the character’s level. For each Hit Die spent in this way, the player rolls the die and adds the character’s Constitution modifier to it. The character regains hit points equal to the total (minimum of 0).
"Regains hit points" is the way the rules usually describe "healing". See the description of cure wounds:
A creature you touch regains a number of hit points equal to 1d8 + your spellcasting ability modifier.
So RAW, being under the effect of beacon of hope at the end of your short rest will maximize the gain from your hit dice.
This is metagaming, and everyone knows this is metagaming.
This is so very obviously metagaming. To be clear, I am not saying this is a bad thing. Different tables tolerate, even encourage, different levels and flavors of metagaming. If you're DM and/or table are okay with this kind of use of metaknowledge of the rules, then go for it.
But this is still textbook metagaming, and probably isn't a faithful in-universe representation of a short rest. This sort of rules application has some pretty odd in-universe implications. That was a pretty tough fight, now you're down 40 hit points. You sit down for an hour. You feel terrible for that whole hour then the moment the hour is up, you instantly go from feeling terrible, to feeling fantastic. And then, we take this understanding and apply it beacon of hope so we can maximize that instantaneous healing we received and feeling terrible for an entire hour. This is not the knowledge or experience in-universe characters would have. This is not how the world works in-universe, at least, not the worlds I DM.
Beacon of hope is, in my estimation, intended for discrete, observable instances of healing, rather than short rest healing, which is in-universe a continuous, unobservable healing process. For these reasons, I would not allow beacon of hope to apply to short rest healing in my games.
But again, if you want to allow it, go for it. It's your game, do it your way - RAW agrees with you.