Kman9:
The power cycling when starting the car is an easy fix ($10-$15). Just power the DC-DC converter from the constant 12v of the car. Run the DC-DC converter output through a relay (the normally open contacts), then power the coil of the relay by the ignition 12v. Choosing the relay is the only "thinking" part of this modification. Since you need to delay the opening of the contacts (that are closed when you are in ACC or run) when the car is started, you will need a time delay circuit in the "fix.". If you are handy with electronics, just use a 555 timer circuit for the relay (design it so you can easily adjust the time to your preference). If even a supper simple 555 timer circuit is too much for you, then just choose a relay with a high impedance coil and add a capacitor across the coil to hold it closed for a few seconds (the capacitor will need to be isolated from the ignition 12v with a diode, otherwise other accessories will suck its voltage and it cannot do its job supplying voltage to just the coil).
As far as "I'm estimating at the plug voltages," why estimate? Open up the cable near the miro-usb plug (within an inch or two, don't cut the wires, just remove the outer insulation), then you can add permanent pigtails from the red and black wires and run through to a connecter that you can access whenever you want (or for $1.50 you can get a self powered volt meter from China and leave it connected permanently). Alternatively, if you do not want permanent pigtails, just (carefully) stick a pin in the red wire (through the insulation) and a pin through the black wire (again up near the plug) and measure the voltage drop at full load (i.e. when the tablet is needing 2A+). If you use the pin method... After you get your numbers, remove the pins, close everything back up, and make sure there is absolutely no chance that any wires are exposed and that the positive and negative and the ground wires are all intact (no broken strands and no visible wire). Alternatively, if you are rooted, I have to believe that someone has an app that would let you measure the input voltage at the input (not just battery voltage), but I have not looked for one. Obviously this number is available to the firmware, because that is what controls the N7's internal supply that makes batter charging decisions. A third, and MOST PREFERABLE method to fix the voltage drop issue, is to just make a custom cable that uses 16ga or 18ga wires for the positive and negative feed right to the miro-usb connector, then you have no voltage drop!
The problem with the voltage drop is that it is NOT consistent. The drop is dependent on the current and that is constantly fluctuating. The N7 is perfectly happy with 5.3 volts (if that is actually what you have, but unless you measure it who knows), but if 5.3v is what is needed at 2amps, then, depending on you voltage drop, the voltage might be as high as 6v with no load. The N7 will protect itself from over voltage, but in doing so, it may shut off. (or go on battery). Since it is not drawing current from the supply the voltage will remain too high until you shut off the car, and start the whole cycle over again.