I wanted to comment on the question in order to ask more information, but apparently don't have enough points yet to comment, so will just "answer" your question.

A normal corridor variance swap spread would have payoff 

$$ 
\int_0^T (\sigma_t^X)^2 \theta(X_t - K_X) dt - \int_0^T (\sigma_t^Y)^2 \theta(Y_t - K_Y) dt 
$$

where $X_t$ is say the SX5E and $Y_t$ is the SPX, $K_X$ the lower corridor for SX5E and $K_Y$ the lower corridor for the SPX, and $\sigma_t^X$ resp. $\sigma_t^Y$ the vols of the two indices, $\theta$ is the Heaviside function. Note that I only have a lower corridor but could just have easily included an upper as well. Do you agree with the above payoff for a normal corr varswap spread?

The corr varswap spread you're trying to value on the other hand, has the following payoff:

$$ 
\int_0^T (\sigma_t^X)^2 \theta(X_t - K_X) dt - \int_0^T (\sigma_t^Y)^2 \theta(X_t - K_X) dt 
$$

Note that the term $\theta(X_t - K_X)$ occurs in both integrals now. Is my interpretation correct, before I continue trying to answer your question?