I think the things you have said are correct... and keep in mind the actual " glowplug light" has little actual connection with the glowplugs working.. are you using the 45 seconds of the key in the glowplug position ? They keep heating for about that long after the light goes off even when it is working normally ( like the 15 seconds)....
But you are correct that a normal engine Turned fast.. should start without the glowplugs AT ALL.... not easy on the starter sometimes... but the physics are there in the FAST compression of the gases...
So at this point I really suggest you get a new battery and be sure the wires connected to it are connected WELL . The chances of " flooding" are one in a zillion.. go for the simple things like your engine is not turning over fast enough to give you combustion temps ... then check your fuel filters.... do you have the clear " inline fuel pre filter' ? Any chance you have algae in your system ? Are you sure you have fuel in your tank ?