I have always heard and understood that a device will only draw as much current as it actually needs as long as the voltage supplied is correct...
That is true, but please do consider the situation where a circuit fault occurs.
How about a simple short somewhere along that DC line?
That could happen due to a failed solid state junction, perhaps a diode, perhaps a transistor, could happen if a capacitor shorts, or might just be due to a conductive bit of flotsam and jetsam getting in there on the board and crossing the right two points.
If there is enough Current available it will be there to perhaps burn circuit board traces away, or depending upon where a short to ground may occur, such as in a solid state junction, the excessive current available could get costly in terms of component failures that would not happen with the designed supply, which in this case is apparently a simple memory cell.
Now, since this is an Internet Forum, I fully expect somebody to come along and state that they used XXXX capacity external battery and swears up and down that it works. Well, it may work, but they just haven't had a fault that could cause the aforementioned problems.
Don't "fix" it -- REPAIR it. There's a Service Bulletin for this one, issued by the mfr. The same guy who doesn't follow it and incorporates this added battery scheme is likely the same one who will post bad reviews about the mfr and product when it fails. Don't be like that guy.