Well I filled a bug report recently about issues I had using the compositor in the VSE. Ton replied suggesting that it was not really built to do that. I suggest that you cut the shots together first then send that cut out to the compositor for correction as it is to slow the other way around.
A little addition to this that may be useful is that as tranform strips are the length of the video strip there useful for primary corrections on a shot by shot basis then to apply a ‘look’ over a wider group of shots or the whole edit by adding a colour strip above the transforms, setting its color to mid grey ie. 0.5 value and blend mode to Multiply then the multiply value to 2.0 to make the strip in affect white, the alpha value for multiply, then add a colour balance to the color strip and create a ‘look’
Have to do the mid grey + multiply by 2.0 to circumvent the color balance refusal to affect shadows ie Lift on a white clip.