[BRX]

I'm just talking from the end users perspective, but as a pianist often working form the chords I just want to say A/Db feels wrong to me in any circumstance.

I don't think you can or should disregard the "key signature" or rather scale of the chord. If it becomes an A by way of transposing or otherwise the root/slash chords should be from the scale of the new chord (so always a C# for the A chord, never a Db).