The problem is that in the corner where the gap is connected to the "volume", the inflation layer gets compressed:

Problematic region

I guess that this is because the inflation forces elements to have their thickness (normal to the "wall") to be not greater than its length (parallel to the "wall"). However, I could not find if there is any parameter that can "relax" that requirement. 

If there are less elements across that face, then the problem becomes less severe:

Problematic region with coarser face mesh

However I con not use this workaround because I need to maintain the number of the elements in the gap on that face which is a critical region for the model. And in general would need to maintain some independence between the mesh in the "gap" and the thickness of the inflation in the "volume", at least to some extent.

Is there a workaround to have the thickness of the inflation layer unaffected by the surface mesh on that narrow face?

Thank you in advance.