Most DMX controllers are 19" rack width so not exactly tiny but there is the ADJ Wifly NE1 which appears to be about 1/2 that width. I have never used one but this appears to check off all the boxes and then some, to get the most from moving heads you really should have a controller that can generate movement effects. This unit can further simplify things if it's combined with wireless recievers on each fixture or on each stand at the very least, do check to see of this requires ADJ specific devices or if generic model will work. I regularly do lighting with nothing but wireless links between the controller and fixtures... many events in very large spaces and with no issue, so you should not have any problem with everything on stage.

Failing that the other obvious solution is to use a phone app with a wifi-dmx bridge, you should be able to do everything you want with that and it too minimizes the amount of cables you have to run... which can be the most time consuming thing about lighting.
Most of the fixtures I own have wireless DMX built-in, I have added it to others and also have some plug in wireless XLR recievers for the moving heads. I do have a couple hardware controllers but use software on a laptop as well, it just depends who is operating the lighting for an event... me or someone else that is less knowlegable.