Funny enough that you come with the same idea as me, I have a though about the Zoan user the last days too and my though about it:
I think the Zoan awakened user don´t just get recover power, I think the one who awakened his zoan power get a "final" form as Chopper, like his Monster Point:
I don´t know but I think with Rumble ball Chopper was able to leave out the hidden power of his zoan df.
Which this he could use the Monster point which make him more durable,faster,better reaction speed,stronger and give him also insane endurance.
I like the idea that Chopper Monster point is the way off from Oda to show how great Zoan awakened user could became using it, just read what Chopper gain:
Before the timeskip, the consumption of three Rumble Balls in under six hours gave Chopper an additional Rumble Ball transformation, appearing to be a combination of all Chopper's Points except Brain Point (Heavy Point stance, Arm Point strength, Walk Point speed, Horn Point horns, Jump Point legs, and Guard Point hair).
Each awakened Zoan user would be kinda different though how massive he get a boost and how strong he became with his third and last form, like monster point.
Attribute which a awakened zoan would get is what I write for Chopper above:
Durable,faster,better reaction speed,stronger and give him also insane endurance, as addition they would became personaly abilities like King fire,Jack water absorbing or Queen Plague(can be happen or not).
And as Chopper monster point they would get a timelimit, otherwise he would be kinda to op to handle a awakened Zoan user, it would like facing a limitless Boundman which can´t be happen:
It is now the only form he needs a Rumble Ball for and, by eating one, he can stay in it for three minutes. However, it still requires a colossal amount of energy to use; after reverting to normal, Chopper is too exhausted to move for approximately 2–3 hours.
Source:
https://onepiece.fandom.com/wiki/Hito_Hito_no_Mi
How this timelimit could look like, I make a seperate post already in the last days and my though how it look like if Oda decide to give awakened zoan user for the flyers aswell:
Flyers Awakened zoan user: Can be use for 30mins/after the Zoan user need to wait for 1hour until he can use it again, maximal use probably 2-3times each day.
Calamity Awakened zoan user: Can be use for 1-3hours/after the Zoan user need to wait for 2hours until he can use it again, maximal use probably 4-5times each day.
Top tier Zoan user(Kaido): Can use it for a day/after the zoan user need to wait for 12hours until he can use it again.
Like this I could see how Oda would plan the whole awakened zoan power.
It would be of course a really op powerup, but like Monster point example I could see Oda planning this for awakened zoan users overall.