How many of your requests were approved or denied?
I will answer your last question first, it's easier. I have had like 3-4 authorizations denied, several canceled/rolled into 1 authorization and like 20+ approved.
So looking deeper I see what you mean, the authoeizations do state, on page 1, under Standard Provisions: 1st section. "The application made for this certificate shall be attached and become a part hereof."
So lets start with I am not a lawyer, so none of what I am about to write can be construed as legal advice.
Without seeing your application I don't know exactly if this boxes you in or not. It sounds possible you may be screwed in a very strict interpretation.
If you stated in your application you are only going to use a certain model/registration number I think a strict view is yes, you can only use that.
There were fields on the old 107 Waiver Portal that asked for a UAS by registration number. Again I am like 90% certain it was an optional field. Plus the new dronezone authorization applications don't ask anymore.
I have not tried for an airspace waiver or operational waiver on the new dronezone so maybe they ask for a specific UAS on those.
Anyways point is, you did not have to restrict yourself to a particular UAS for a successful authorization, so the intention of the FAA (personal interptetation) is to allow for one authorization to cover multiple UAS types/registration #'s
If you are going to take a strict view then when/if you renew the authorizations I would start over and apply through the dronezone from scratch instead of renewing your existing one.
Again, if I saw your application I might have a more nuanced interpretation. I am not asking you too post it, but without seeing everything I am guessing a bit.