In combat can not pick up (ie: no F)
Out of combat pick up causes 0 cooldown (ie: could immediately drop again).
This has probably been suggested but I am not aware of it. You can run with your turrets so long as they are not destroyed. They already know when you are in combat and when you are not. I would think it would be little more than adding an IF and call to a function or the like. pickUp{ if inCombat() { coolDown(1.0)} else { cooldown(0.0)}} etc.
Ever tried rezzing someone when your turrets are around or stuff is on the ground? Supposedly the rez shows up first but that is not always the case. This would solve that issue. It would make turret builds more mobile than they are now and nearly on par with other builds as far as mobility other than they cant fight on the run. Your still even going to have to run around and collect them. While marginally painful isnt bad.