I'm not an expert on these things, but if the slopes differ, I think you could fix that by just adding more variables by including the group-by-covariate interaction. So each group would have its own slope. The disadvantage of doing that is that certain effects might not be interpretable as a result.
One issue, though, is whether the groups differ on the covariate. In that case, you shouldn't use ANCOVA in an attempt to "control" for the confounding, though unfortunately this is a popular thing to do. I've posted previously about this, e.g.:
https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=SPM;ba279a8f.1108
|