If you have big surf where you ride you probably going to want a standard shortboard shape with three fin set up and some rocker to it. Not an easy board to learn to surf on especially if you found padding a bigger board a challenge. Sounds like your going to be better off with two different boards for a while. I bet you can find a second hand bigger surfboard for pretty cheap. You dont have to worry about strength much as your not kiting it, and spend your money on a strong built kite surfboard with straps. something like this will work nicely, but there are plenty of other options.http://oceanrodeo.com/kiting/surf-series-511-board
Firewire or any of the other big kite brands have kite built standard shortboards that will do nicely. Talk to a shop and they can give you some advice on sizing.