Hi @NamelessPlayah93, sorry this reply is almost a month late.
My findings:
1. There doesn't seem to be a block (species ID or perhaps some kind of table) that the game uses to base the next spawn off, additionally...
2. You can actually soft reset the spawn by saving after you defeated the Stellar Tera, save in the area, then reload the game when the date changes (the date only has to change once; it is unlike SWSH's system where the species is preset for the next 3 raids)
As such, there is no way to force the game to completely generate an encounter based on species.
(Example: you can't change a value to 'Altaria' and it generates all of Altaria's details, such as PID, IVs, moves, etc)
Do note:
I am able to manipulate the Fixed Symbol Encounters, and change Stellar Haxorus to Stellar Altaria, but the way of doing that is by fully injecting a well-formed Pokemon (minus OT details and marks), which at that point would be the same as what @Atrius97 said:
I could just swap in all the details but retain generated PID/IVs/EC etc, but I believe that cause issues relating to the legality of RNG generation down the road (presumably the RNG generation includes species) so I am not fully comfortable with that. My advise is to soft reset away.