So if I clamp off as soon as the pull is complete will I get the same string bed with a crank machine. This takes the constant pull out of the equation.
If you're trying to get the same result with your constant pull machine as you get with your crank machine, as far as the stringbed stiffness, the right way to do that is to just reduce the reference tension setting on the constant pull machine by possibly 5 to probably 10 percent.
You shouldn't have to wait 20 seconds for the string to stop stretching, it doesn't take that long (maybe 5 to 10 typically, especially if you've pre-stretched the string).
Anyway, the problem with doing what you're suggesting, clamping "immediately" with the constant pull machine, is that you'll get wildly inconsistent tension string to sting doing it that way.
The string stretches the most quickly right away, then continues to slow asymptotically until it essentially stops.
If you clamp it while it's in the process of rapidly stretching/changing (i.e., moving), you're going to let it stretch
much differently each pull, depending on how "immediately" you clamp it, one second vs. two or three.
For consistency, you need to let the string essentially stabilize on every pull before you move on (clamp it).