On the console versions, you can sometimes get away with pressing 3 punches and start only.
However, how I have got it to work is thus:
Ryu - roughly 3 secs
THawk - same as above
Guile - same as above
Whoever is under THawk - same as above
Back to Ryu - same as above
Then you can move anywhere else and press Start, IMEDIATELY followed by all 3 punches - much like the speed of doing yoshimitsu's upward launch kick (4, followed by 3, like a pianist does what is known as a paradiddle in case you are ot familiar with that).