so let me address the second case first...
also, if a team is up 3 with 20 secs left, they shouldn't be trying to shoot at all
in this case we have chosen to have the defense foul.. as they must get the ball back in order to have a shot and the clock will run out.
with 1 minute left, up 5, i think you will see every pro team burn at least 20 secs unless they get a layup or dunk
this is a real borderline case.... if there is 1 minute left at the start of the possesion, then the defense will play defense until it gets to less than 45 seconds i think.. then they will foul. So for those 15 seconds, yes its possible that the offense takes a shot.
Let me ask the question this way... up 5, how much time needs to be on the clock in order for you to just continue to run your regular offense? If its less than that time, do you immediately go to hold the ball till the last 5 seconds and take what shot you can get? Do you just increase your threshold for shot quality say linearly as the clock goes down until it reaches some upper threshold? that would sound reasonable to me... but then again you don't want your threshold to be so high that you end up taking a really poor last second shot. Things are somewhat complicated by the fact that generally the shot threshold has been set to go down as the shot clock progresses... you will take higher quality shots earlier in the possession than you would later. So effectively this modifier would just flatten the curve.. or if high enough it might make it inverse.