It seems you're looking for a pin-to-pin replacement, or close enough.
My thoughts:
Using another HC05 is obviously pointless.
The only reasonable alternative to keep changes to a minimum is to move to a S08. Although an S08 is source code and object code backwards compatible to the HC05, that's where the similarity ends.
Memory layout, or accessing MCU peripherals (like the A/D) is not 100% compatible, so some code rewriting will most likely be required. So, if you only have the binary image of the app, it won't be easy, as you would first have to disassemble the code.
Solving pin-out issues is a smaller problem as you should be able to make an add-on mini PCB to convert another MCU's pin-out to your original.
I don't think you would have to write your code from scratch. It's fairly easy and straight forward to convert HC05 code to S08, and to also take advantage of the new capabilities. However, you would need to have the source code. Do you have it? In what language?
(BTW, I may be able to help with the conversion as I've done this many-many times already.)