How about Al Wasl hospital which is a govt hospital and of course Rashidya which has excellent care.
I would be more worried about having a home birth without medical support where you may find you end up paying more if there is a problem. I had a friend who had a good experience at Welcare. I think they paid 8k for a standard birthing package (lump sum - no c-section or extras like incubators etc. Included 2 nights stay)
Best of luck. How stressful!
As far as I am aware home births are illegal here. I think you would have great difficulty getting a birth certificate for your child. Hopefully others will have more useful suggestions.
What about Al Wasl hospital - it would be much cheaper and I have had many friends who have delivered there quite happily.