You won’t be able to do all of that in just an overpass query, you’ll need to do some post-processing using other tools/scripts.
(Getting the data for all members in order including duplicates might be possible in overpass alone, but certainly not correcting out-of-order ways)
As I have tried it today, technically I guess you may be able to “abuse” Postpass/PostGIS to try to sort it? Not exactly Overpass. Certainly not really what it’s designed for. Easier to postprocess in other applications.