It seems that although the BVAR add-in correctly calculates the parameters when including exogenous variables using the Sims-Zha Normal Wishart prior, it does not report them correctly.
If one compares the results from EViews with those from the "R" programme "MSBVAR" (which was the basis for the original add-in) in this situation, it seems that EViews picks up the value of the estimated constant and places it in the table position for the first exogenous variable, then displacing all the other coefficients downwards one row, so that eventually the reported constant is actually the coefficient of the last exogenous variable. This should be easy to fix.
Whilst on the topic, is there any reason not to allow exogenous variables in the SZ Normal Flat or the Flat-Flat priors cases? (I ask because the MSBVAR programme permits them - non-null "z" matrix with "prior=1" or "prior=2".)