Ah-ha. Good luck to you then; please let us know how it goes. I plan to get the card issued airside at T1 next Thursday night; I will try to remember to ask them what the operating hours are.

Please keep in mind also that you are running some risk. If they don't allow you to go backwards from T1, then you will have to go through immigration and come back. Even if you use the e-gate to enter Dubai, you won't be able to use the e-gate to exit (or vice-versa), since you cannot enter and then re-exit on e-gate within six hours. You can play dumb (and avoid the lines) by going to the immigration agent at the e-gate area in either T1 or T3 and saying that your e-gate won't work, but they usually stamp your passport there.