I have seen companies advertising in Gulf News that take the hassle out of the process by doing a medical test in their own clinic and then delivering your visa stamped in your passport within 48 hours.

Don’t know what they charge though and looking at Seabee’s experience, it might not be necessary.

The only real hassle was the queuing at Immigration. That and finding out in advance what was actually required!
If you go to Jebel Ali clinic the medical is very quick and easy. The other places have big queues.
Emaar can only sponsor one person and you have no option except to go through them for that visa. But they wanted another Dh5,000 to do my wife's visa even though I have to be her sponsor, so I thought I'd put up with the hassles at Immigration to save that fee.
Also, the Dh10,000 deposit you have to pay Immigration for wife's visa applies regardless of who does the visa application for you.