Haven't used Driclime, and there are nylon weaves like Supplex that feel more like cotton than the 1.1 or 1.9 oz riptstop nylon sold for tents and such.
But if you are set against nylon, and want something with a very soft hand (totally not stiff), even a bit fuzzy, there is this fabric in dark olive that I purchased last fall when they had it in sage: "Dark olive green showerproof polyester pertex" from fabrics-n-stuff.co.uk.
It weighs around 1.4 oz per sq yd on my scale, is slightly water resistant, is polyester, and costs 3 British pounds per running meter. Haven't used it in the field, so cannot vouch for its durability, but being a polyester, it is likely to be less durable than nylon for a given weight.
There are warnings on the web about this company, and you may have to go through Google to reach their site, all of which may have to do with its use of the trademark "pertex;" however, I ordered from the US and received delivery to my PO Box within a few weeks. Suggest emailing them before ordering to confirm availability and terms.
Quest Outfitters used to have Versatech, a 2.8 oz per sq yd polyester, lighter than 3.4-4 oz Supplex, which they recommended for sleeping bag shells and liners. Might be worth a call or a Google search. They probably still have the heavier Supplex. The people at Quest and OWF, have often been very helpful on the phone.
You might want to order samples before spending enough for several yards/meters.
You can eMail me at email@example.com, and I will send you a sample of the UK fabric by post.