Who says the firmware supported the disk directly and an option ROM or DDO (ie software-loaded option ROM, like the modern "XTIDE Universal BIOS" and "optromloader") was not being used? 😀
Anyway - how the numbered presets work is that the information is stored somewhere in memory (computer's ROM or drive controller's option ROM) in this format: http://www.minuszerodegrees.net/misc/at_fdpt.pdf and by the time the OS is launched, interrupt 0x41 points at the appropriate preset for the first HDD
So a possible approach would be to select type 1, find out what address interrupt 41 is pointing at (if I did the math right, that would be found at 0000:0208, so you read 8 bytes from there to find the address, then you read 16 bytes from there to read out the settings for type 1), repeat for type 2, then dump the appropriate ROM and try to find those bytes there, hopefully they're consecutive...
I'm fairly sure there's a program that automates this but I can't find it 🙁 , or rather I have found https://aeb.win.tue.nl/linux/hdtypes/hdtypes-1.html which seems to do that but isn't the one I remember and running Linux on that PC will probably be a bit hard 😀
Update - it seems to be GSETUP
There won't be 99 settings I hope, 46 (minus one, as "15" is used to indicate "look at another SRAM byte to find the 16-or-higher setting) was traditionally the maximum before most firmwares gave up and added custom type 47 😀
In fact, could it be that your firmware only supports 2 types and the following ones are reading from other-purpose-bytes in the ROM?