Is the backwards compatibility seamless and simultaneous?
Able to reply to both mode S and mode 3 interrogators in real time?
Or a toggle switch between modes, in which when mode S is selected mode 3 interrogations will be ignored?
No - a Mode S transponder will respond to interrogations by a "pure" mode 3 interrogator. ...
I think the problem is that you see a Mode 3/A (identity) reply, but you try to interpret it as Mode C (altitude reply).
In Mode C, altitude is Gillham encoded, using all pulses except for D1 and X. This gives a range of -1200 to 126700 ft in 100 ft increments.
If you see a D1 pulse, you are not looking at a Mode C reply.
In Mode A, a 12 bit identity (...