[sciurius]

I am not transposing keys, [...] The transposition interval is derived as the difference between the base pitches of a "from key" and "to key",

That is what I would call transposing based on keys.

but it can be set perfectly fine without any keys at all

If you mean by specifying intervals as `(-5 -9)` I would rather use 'keys`

Summarizing:

• Transposition is defined by two reference pitches, the source pitch and a destination pitch.
  
• The chord name (including a bass part) the transposed same way as the source pitch transposes to the destination pitch.
  
• Double flats and sharps are replaced by their enharmonic equivalents.
  

For practical purposes, the current key of the piece can be used as source pitch reference, and the desired key of the piece can be used as destination pitch.