I agree that you would want to stretch the muscles used as much as possible. If a client has a particular over tight muscle group or groups that is causing issues, you could stretch that group or groups first and then do other muscle groups as time allows.
It is pushing people with limited time to ask them to try to do more later and likely to be met with limited success as well. But I would at least approach the subject of taking a brisk walk berfore/after dinner. And then strecthcing properly after the walk (bike ride, swim, etc.) to get the muscles prepared for a stretch intended to promote ROM/Flexibility. This will also give them a second bout of exercise to help increase their fitness and other benefits depending on their goals that may encourage compliance.
And as stretching is one of the most frequently omitted pieces of the exercise puzzle, it is important to impress upon clients how counterproductive it is not to stretch. While there is a great deal of controversy as to stretchings contribution to fitness, a wide margin separates the science that has shown benefits and importance compared to the very small amount that raises questions as to effectiveness. I could go on (and on), but will end here. Anyone reading this that would like to discuss it further, please feel free to contact me through my profile.