Unfortunately, you are on your own here. We have given you the theory you need to accomplish what you are trying to do, but the specifics of your shooting situation are so highly variable, that we cannot give you any specifics. Let me recap a few concepts for you.
1. For flash (without shooting high speed synch), the fastest shutter speed you can use will be your camera's synch speed. The flash burst will be shorter than the length of time that the shutter is open.
2. The Einstein 640 and small flash have somewhat similar operating characteristics. The higher the power level, the longer the flash duration. When looking at stopping motion, always look at the t.1 time (i.e. the length of time that 90% of the flash). This behaviour unique to the Einstein units (other studio flash units may also perform this way, but I am not aware of any. Other types of studio lights tend to have the shortest flash at maximum power and the length of the flash increases as the power output decreases.
The Einsteins have two operating modes; Action Mode and Color Mode. The Color Mode is what I normally use as it provides the most consistent colour temperature between shots. You can sacrifice a bit of colour temperature repeatability for a faster flash by using Action Mode. The only time the two modes give you identical results are at full power.
http://www.paulcbuff.com/e640.php
3. Small flash (speedlights) tend to have a maximum output that is an order of magnitude lower than studio flash. This means that speedlights are going to give you a lot less light output than studio flash. Your Einsteins have a maximum output of arond 640 W-s whereas a high end small flash is going to be in the range of 70 W-s.
4. Changing the shutter speed to a setting that is lower than the synch speed for your lights will have no impact on the amount of light from the flash that affects the image, but the longer the exposure the more the ambient light will come into play. As has been mentioned in previous posts, the colour temperature of the studio flash will be different from the ambient light from the stage lighting.
Note: This published synch speed applies to small flash only. Studio lights tend to fire more slowly and you might have to use a slightly slower shutter speed.
5. High speed synch (HSS) will cost you around two stops of light. I know PocketWizards suggests that you can use the Einsteins in a HSS mode. I have tried to do this with my units, but have not had any success. As Bill has noted in his reply, you will lose 2 stops of light in HSS mode. This mode seems to work well with my Nikon Speedlights.
6. If you are shooting with Einsteins, the best way to freeze your subjects would be to shoot at the highest speed at or just below the published synch speed of your camera + use the lowest power setting you can get away with. This will tend to push you to a wide aperture setting, so you will be dealing with a narrow Depth of Field (DoF).
Bill has gone over this in the other thread you posted in:
Shooting dancers in stage light or use flash? Or mix?
7. If you wish to check out the amount of impact that the ambient studio lighting has on your image, shoot the camera at the shutter speed / aperture setting / ISO that you plan to shoot at WITHOUT using any flash. That will show you the contribution that the ambient light makes on the image. If it is too much. either turn down the ambient lights or reduce the aperture until you get a black image.
8. Shooting mixed light can give you interesting images as the ambient light will give you a blurred image and the flash will freeze the dancer. Look at the front curtain / rear curtain (Nikon speak) or first curtain / second curtain (Canon speak, if I remember correctly), as this setting give you totally different looking results.