After much searching I finally found kayak sail that I love for my Advanced Elements Convertible kayak.
The Kayaksailor. See photo below (I hope to eventually post a UTube video):
I had previously tried the Windpaddle. It has the advantage of light weight and low cost. I have succeded in sailing somewhat upwind with the Windpaddle, but not enough for a round trip and with much leeway even when using the paddle as a leeboard. It is also hard to control in shifty wind and hard to paddle while sailing.
So, my quest for the holy grail of kayak sailing continued and finally brought me to the Kayaksailor (you can Google them). Kuvia LLC makes two sizes 1.6 sq m and 1.4 sq m (to fit different kayaks and wind conditions) as well as an add on Genoa kit. Kuvia LLC also offer excellent customer support.
The Kayaksailor sail kits are very well designed and very well balanced. They can be mounted on an inflatable kayak. The key to the rig is the pair of integral adjustable leeboards. The kits are very professionally made of high quality materials. The Kayaksailor kit is a completely collapsable sloop rig with a battened mainsail supported from the mainmast by a topmast. It is designed for kayak sailing upwind (and of course other points of sail) and allows for paddling alone, paddling while sailing or sailing alone. Kayaksailor rigs perform very well and are easy to use.
No, I do not work for them, I am just a very satisfied customer.
At last I have succeeded in sailing the kayak around in circles.