The Shinko tires sound like a great tire for a great price and it seems like 2/3 of my riding is on wet roads. I have noticed a little shimmy riding along road seems when wet on the Dunlops. Also have to be a bit careful downshifting to avoid rear tire slippage.
One consideration is that I want to stick with the stock size. This bike is on the verge of being to tall for me and a taller rear tire would be unhelpful. Also, in spite of all the hoopla about it, I really don't find getting the bike onto the center stand all that difficult.
If 2/3rds of my riding was on wet roads, I would go with a Michelin PR3 or Pirelli Angel GT up front, in the 110x80 size and the Avon Azoro(I know that is not speeled wright) on the back, and I really don't like Avon Tires. You really need to consider focusing on the safety aspect. Wet roads are slippery, you need all the grip you can get. An extra $100 in the bank ain't a gonna help you iffn' yer dead.
Note: If you do some sniffing around on tire manufacture's sites, you will find that the 110 front is a better fitment for the wheel. The stock Dunflop front in the 120 size actually measures out closer to a 130. A 130 can fit the rim, but the 110 fits better, and handles better, without being squeezed.