I was banned by my previous employer too. What I did:
1. Ensure that my resignation letter was received by the employer representative (our HR in this case) to prevent them from claiming that I have absconded.
2. I've worked for 2 years in this company on unlimited contract and coz no NOC, was given a ban of 6 months automatically by the Labor Dept.
3. A week after the end of my 30 day notice period (I have stopped coming to work altogether), my previous employer cancelled my visa and released my end of service entitlement at the Labor Office itself. The officer at the Labor Office will usually ask you if you got your money before they would stamp the cancellation. My employer, being aware that my resignation is signed and therefore accepted by them, have no choice but to cancel my visa. A colleague who also left them was not successful in getting the resignation signed, instead he presented the letter to the Labor Office and the Labor Office send them a letter to appear in their office and thus my ex-employer, having have enough of this case, again was forced to cancel his visa and yes with ban.
4. After cancellation, the employee have 30 days on which to change his/her visa either to employment or visit visa. I got mine changed to employment visa 2 days before the 30 days expires (yes, I freely roamed around UAE during these time). I was asked to exit though to change my visa but bringing with me the original employment permit and was only on airport to airport (meaning I came back to Dubai at the same day). Yes I did pay for the airfare, but eventually, my reimbursement for the airfare was approved and I got my money back.
5. How our PRO (he's a local) left my ban, I have no idea, he just give me the employment permit and asked me to get on a plane as he does not have enough time to have my employment visa stamped on my passport. He did told me though that I gave him lots of headache
I hope this helps.