A prerequisite to Transposing Harmony like a musician is to conceive and hear the music in functional musical terms, not just as an arbitrary sequence of dots…
Consider, for example, the standard chord progression Dm7-G7-CM7-Am7.
The key to success is to understand this chord sequence in functional terms… in other words as ii7-V7-IM7-vi7.
Then, if you want to play it in another key, all you have to do is think and play “-ii7-V7-IM7-vi7″ in the new key.
In other words, you do not “transpose” at all. You simply play those functional chord changes in the new key!
No brute force calculations.
Not counting half steps.
No mental gymnastics required!
What IS required is the deep understanding that comes from mastering scales, chords, and chord progressions in functional terms and as meaningful patterns with your intellect and ears fully engaged!
You will learn lots more about on your study of chords and chord changes.