Your problem is quite a challenge. I would consider another membrane roof over the whole floor; but, this time, I would use the fiberglass base that makes the roof pitch more pronounced. Fiberglass is available in various tapered thicknesses to make a continous pitch for drainage. The only problem is, I don't know how well it will stand up to foot traffic and especially to chair and table legs. I know that some roofs have several thick pads for walking paths, like stepping stones. If the chair and table legs were placed on something to disperse the weight there may be no problem at all.
Sorry I can't be more definite about this; perhaps you can google the product and find out how much traffic it can stand.