I have been playing through You'd Be So Nice to Come Home To. I have a pretty good grasp of the song and the chord functions up to the final section. I am interested to know the function and substitutions for the final 8 bars. 

My lead sheet has it as: 
D#diminished7, C/E, G#diminished7, Am7
D9, Ab7, D7b9, G7, C6, Bm7b5, E7b9

Where are these chords coming from, particularly the diminished chords, what was the thinking behind these substitutions and how would you approach playing over them?

Thanks very much!