You said that the voltage is dropping to 13v when it is on load, which supports that theory. If the ECU is monitoring voltage and is looking for more than 13v and is set to chuck a spaz when it doesn't see what it expects to see (i dont know how the 5g works in that regard) then yes, that all fits.
You can't go too big on current output from an alternator btw, it's not like voltage - the car will only draw how many amps it wants to draw. if you fit a 200 amp alternator and the car only wants 105 amps, it will only draw 105 amps. So fitting an uprated alternator will not blow anything up. I fitted a 4g alternator to my 3g (the 4g one has a higher max current output).
