To buy yourself a little time while trying to decide, you at least need to put on an aftermarket exhaust and intake on your 350. You are still stock on it and the aftermarket pipes makes a huge difference in power and will satisfy your need for speed a little longer. This will also give you time to save a little more money so you can take a bigger step up. I agree with DSW, the Z400 is a nice bike but it is not a huge step up from the 350. I think you would be happy with the Z400 for a while but will then wish you went a little bigger fairly quickly.
Keep your options open. The 660 is an awesome bike, although some think it is tippy but it has power to spare. The Predator 500 is an awesome bike too. The 2005's have reverse and have fixed almost all of the quirks that the '03 and '04's had. They have upgraded rear axles and Fox suspension and are fast as hell.
You can get some great prices on both of these bikes used.