The AVC working as you described is about all one could ask for. Doubt that the original part would perform much better. The AVC compensation range isn't that wide, so it's kind of a subtle feature anyway. It will work best on strong stations- weak ones don't generate enough error output to do anything noticeable.
One thing to look for is symmetry- does the AVC compensate equally when mis-tuned both high and low by the same amount? If not, this can be adjusted by twiddling the slug in the transformer that you replaced.