D-|-----||----------------------------0----||
A-|-5-3-||------------------------------3--||
E|-----| |*---------0---------------------*||
D-|-----||*-3-0-----0------3/5--3-(0)-----*||
A-|-----||----------0------3/5--3-(0)------||
D-|-----||--------0----0-0-----------------||


D-|--------------------|----------------------|-0---------|
A-|--------------11-13-|-/15-11-13----11------|-0---------|
E|--------0-/12-------|-----------12-----12\-|-0---------|
D-|-3-0----0-----------|----------------------|-0---0-3-5-|
A-|--------0-----------|----------------------|-----0-3-5-|
D-|------0-------------|----------------------|-----------|

D-|-------------0----|
A-|---------------3--|
E|------------------|
D-|-/7-3-5-0-3-------|
A-|-/7-3-5-0-3-------|
D-|------------------|...and back to the verse (which is all D7)


The part we discussed:
These sets of voicings all work (but it looks to me like he's using the second set in 
the video):
D-|-0-0-0-0-|-7-6-5-4-|-0--0--0--0--|
A-|-3-2-1-0-|-0-0-0-0-|-15-14-13-12-|
F#|-3-2-1-0-|-6-5-4-3-|-15-14-13-12-|
D-|-0-0-0-0-|-0-0-0-0-|-0--0--0--0--|
A-|---------|---------|-------------|
D-|---------|---------|-------------|