Another experience to add to the list.

I found this easy (I'd previously held a regular e-gate card issued before arrivals in T1, and renewed in the office upstairs at T1, but these had expired). Once through arrivals in T3 I headed upstairs to the economy departures area (the lifts are the quickest way) and went to the Residency/Visa Desk - I'm not sure what the right term is, but a small office with desk right in the middle of the concourse before entering any of the checkin areas. It's near the duty free shop.

Go to the left hand counter and they will help you, they can issue both regular e-gate cards and put your details onto an Skywards Gold card. Took only a few minutes.

As a general comment I've noticed there are some snide remarks about service from Emiratis on immigration counters etc. In my experience on many, many trips through the UAE a smile goes a long way, and getting my e-gate card is no different. Lighten up folks!