The above advice is excellent, but personally I'd be concerned about the failing joinery at the aprons. Dowels?
I'd thing it wouldn't be too difficult to break down to individual pats/assemblies and rebuild/finish.
Of course anything you do will take away some of the character.
I faced the same issues with an old family desk that had been repaired in everyday possible, right down to nailing everything.
The owners didn't car so much about the "originality", they just wanted the desk to be presentable.