So... how do you guys photograph hummingbirds?
I don't. We've never had (or noticed) hummingbirds in our garden here until just about three weeks ago: two of them stopped in while heading down your way for the winter.
Maybe next summer, then.
But I would use my DSLR, a 200-300mm lens from the collection here, and the big external flash. The old 40D I have here only goes down to 1/8000th of a second, but that's probably quick enough.

EDIT: Note that at 1/8000th of a second (or anything beyond about 1/250th), the shutter is never fully open at any one instant.. so using a flash at those speeds can be troublesome, since the flash duration is probably less than 1/8000th.
My camera and flash have "high speed sync" capability, whereby the flash fires multiple times (VERY quickly) as the shutter opening moves across the sensor, illuminating the entire sensor area in segments. But this probably is a bad thing for a moving object like a hummingbird.
Cheers