Although it has a joystick and therefore is spring-loaded for modulation, the sheer quality of the Roland A800 (which has everything else on your list) is worth checking out although it is definitely somewhat outside the budget limit you mentioned. However, having owned a cheaper controller - whose keyboard velocity response I could *never* get to work quite right - and which eventually just started flashing up random stuff on its LCD display - I would say that the A800 is a purchase I definitely will never regret. Since it has aftertouch you can also map this to modulation and I personally far prefer a joystick since you can bend and add modulation or another effect with one hand, something that is awkward at best with separate pitch and mod wheels.
Since you said a lot of keys isn't important you could of course then go for the smaller and cheaper A500 which only differs in key count. However the advantage of a 61 key controller is that it is big enough to play anything except classical music
You get a full set of transport controls, 9 knobs, 9 faders and 8 velocity sensitive pads. Admittedly Roland aren't the best at intuitive software design but once you've gone through the one-time pain of getting it set up, that's not a problem for operational use. In fact, having dedicated split,dual, upper and lower buttons makes it very handy because you can map these to different split points and midi channels and easily split and layer sounds in performance. And - as I said - the quality is superb, all the buttons, faders, keyboard etc are not built down to a price. It looks like something that will last many many years.