but I don't know how to convert the set of hex digits the user inputs into memory into the format required for the FAC
I have a strong feeling that this is not about hex, but binary integers, 16 bit or more.
I know about FRMNUM ($DD67) and PRNTFAC ($ED2E), but I can't find the subroutine that Applesoft uses to take a decimal number and convert it to the six-bit exponent-mantissa format.
You're already on the right track. For example GIVAYF ($E2F2 *1) converts a 16 bit integer held in A/Y (High/Low) into a floating point number in FAC.
Of course this is less handy if your numbers are not straight integers, but some format of your own - which brings us to what might bet the primary issue:
Where is your data is originated?
Is it from some internal storage, or user input. If it's from user input why not skipping the task of reading a number, turning it into some two part integer and then convert it to FP and use the Applesoft input routines directly?
On a side note, it would be great if you could not only comment your source (*2), but as well add it not as picture but text. This does not only increase readability, but helps others a lot to reply with code sniplets you might love to get.
*1 - I always loved that address, it's o easy to remember: Enteger to Float too (yeah, I know, silly, can't help)
*2 - I would consider some header describing input/output/task a base minimum to each and every function. Keep in mind, you want to read your code in 10 years from now as easy as it is today - without a need to dissassemble your own thoughts.