>>> I suspect at 1/250, the flash is really putting on the burst. <<<
The shutter speed doesn't affect the flash exposure. The flash burst is so brief, typically less than 1/2000th of a second, and therefore the flash exposure on the film is controlled only by the aperture. So choosing a faster shutter does not require more output from the flash, since the flash burst is already finished long before the shutter closes.
The selection of the shutter speed then only determines the ambient light exposure on the film. If you want the flash to be the main light, with little or no ambient light visible in the image, then select a fast shutter. If you want the flash to be "balanced" with the ambient light in the image, then choose a slower shutter that will give a proper exposure of the ambient light at the aperture that was set for the flash.
>>> The RX can sync at 1/60, 1/125, or 1/250. <<<
SLRs with focal plane shutters, like the RX, can sync the flash at any shutter speed equal to or slower than the maximum sync speed. Therefore 1/30, 1/4, 1/90, and all other shutter speeds less than or equal to 1/125 are usable with the flash.
My advice is to use manual mode for flash exposures. It's the only way to have complete control of the flash exposure and the ambient exposure at the same time.