Is it possible that there could be more than one cause?
I had a leak into the passenger footwell that was caused by an ill-refitted passenger door vapour barrier. This must have occurred following a window glass replacement after an attempted theft. Symptoms were water dripping into the passenger footwell from the inner bottom of the door during very heavy rain. Of course this would not affect the glove box area. I have seen a number of similar reports. I fixed the problem using a £3 butyl rubber sealant tube.
You did well though to clearly spell out the areas affected by the leak - and your doubts about the proposed solution.
F10 530d M Sport, September 2012 Individual Amazonite Silver, Oyster Dakota Leather, Auto, Nav Pro, Bluetooth + USB Devices, Expanded BMW Online, Comfort Seats, Sunroof, Sun Protection Glass Individual Satin Walnut Honey Brown Trim Interior Inside/Outside Mirror with folding and autodip, M Rear Spoiler