Model dv7 3112sa
OK, it's a dv9-3100 series. "HP Pavilion dv7-3100 Entertainment Notebook PC series" In their listings.
Unfortunately, I cannot find anything particularly useful whatsoever- you aren't missing anything here, if that was your original thinking. All the documents refer to using a "BIOS File" but the instructions they give don't give you a BIOS file when applied to those earlier models, they give you that shoddily constructed BIOS update program, which would only be any good when running it under Windows on the system itself.
Now, I presume that the exe file wouldn't work if saved to the flash drive and following the procedure but, at this point, maybe it's worth a shot if you haven't tried.
I found
This related document which just points back at the document you referenced about finding the BIOS file (which is useless for the stated reasons, as you also found).
I presumed that, perhaps the BIOS file was inside that silly "insyde BIOS" utility- which would make sense, as it must be in there somehow. But it's not present as a resource, and the best part is for some ridiculous reason the file is actually packed with some kind of EXE encryptor, because heaven forbid somebody actually get the file they need.
So, I have no idea how to find this fabled "BIN" HP speaks of that is needed to update the BIOS but which HP has evidently not seen fit to actually provide users. A few searches found a number of other people in the same boat. HP support seemed to happily link to the very same document but never in the threads I've found actually addressed the complaint that there was no .BIN BIOS flash data to use.
I presume you've already tried running the recovery? Unless the drive has been repartitioned or you deleted it it should be able to recover from the recovery partition information.