Your camera is limiting your shutter speed to the 60D's maximum sync speed. If you were to use a faster shutter speed, you'd have black bars at the top and/or bottom of the frame, because the shutter curtains would be covering part of the sensor when the flash burst goes off. The only way to use a faster shutter speed than 1/250s with flash it to use high-speed sync or tail sync.

With high-speed sync, the body and the flash (if both can perform HSS) communicate so tha the flash can send out pulses as the gap in the shutter curtain sweeps across the sensor, so the full frame will be evenly illuminated by the flash. This does, however reduce the power output of the flash, by roughly two stops, so there's a game of diminishing returns going on.

With tail sync, (aka "supersync" or "hypersync"), the flash is fired (usually at full power) a little bit earlier than with regular sync, and then the exposure happens at the "tail" of the flash burst when the illumination is likely to be more even across the frame. The timing is critical, and again, you have diminishing returns on the amount of illumination you can get.

Your third alternative would be to place ND filters over the lens, so that you can can still have a large aperture, but use a shutter speed at or below your maximum sync speed.

See also Neil van Niekerk's tutorial on high speed sync on his Tangents blog.