I would have to dig in further (which I don't have time for now), but what I think you're seeing is a change due to the implicit clustering of points on a thick surface....
The mesh points are arranged according to approximately equal arc-length by OpenVSP. If the cluster parameters are set LE=1.0, TE=1.0, you should get equal spacing.
However, think about a cylinder -- equal spacing (in terms of arc length) will actually result in clustered spacing when those points are smashed down to the VLM thin surface.
This image is a default wing. The airfoils have been changed to circles. The point clustering has been set to uniform -- LE=1.0, TE=1.0. Yet when viewed from above (or projected to a VLM surface), the points are clearly clustered at the LE and TE.
So, as you're varying your thickness (everything else held constant) you are actually also implicitly varying the clustering around the airfoil -- particularly at the LE, where the shape has lots of curvature.
You should be able to create two (otherwise identical) propellers. One with thick foils, the other with thin. Change the view surface mode to 'Camber Degen'. Then adjust the LE/TE clustering on one of them until it most closely matches the mesh spacing of the other. Hopefully you can get a fairly similar mesh between the two.
Then run both of those cases through VSPAERO. I suspect their results will match more closely.
Let us know how it turns out.
This may mean that you want to perform a larger resolution and clustering study to come up with good values for your purposes.
Rob