I really doubt that all this extra effort is worth it in the end but each to his own. If the turn order was seen as a problem this could probably be solved by implementing a bidding system for who goes first. Instead of choosing which camels to place you secretly draw from one of five concealed bags. The game ends when one bag is empty. Game ends when 12 oasis tokens have been awarded.
Random elements are the initial setup, random draw of tiles and seating order.
The only thing I can come up with would be something along the lines of bidding how few of your initial 5 tiles you get to choose. I doubt that this would work all that well in practice. On the one hand Samurai seems less random due to the fact that everyone will get the same distribution of tiles. On the other hand there are more varieties of tiles, which makes it less likely that you ll draw the one you want at the right time. There are a couple of tactics that can be used to overcome this however and I personally feel that this is what separates the good players from the bad.