First off, I know this is not a substitute for a professional clean/test, but I think that it would still give an improvement vs in-tank or on car cleaning. Please correct me if wrong.

I was thinking of gravity or probably pressure feeding a cleaner or solvent such as de-natured alcohol (brake cleaner), Techron, SeaFoam, Xylene, etc. through the injector while connected to either a 9V battery or 9V+2AA batteries for 12V to keep injector open. Would this help to clean out the injectors without causing any damage to them?

Again, I know this is no substitute for a professional cleaning, I just want to know if this would be more effective than an in-tank or on-car cleaning, while still being safe for the inectors?

 

I wouldnt do that - I would find a way to pulse them on and off while squirting the cleaner through them. If you leave them on you might overheat the coils - although I am not sure what happens to the coils at low voltage. If I was going to set up a rig at home to clean the injectors I might just use a fuel rail and manifold setup and pump and switch the injectors with some kind of inexpensive PLC. You would have to do a buch of cleanings to pay for it unless you got one for free somewhere.