Bizarre scaling issue

I’m making a model that is supposed to have dimensions of several centimeters, but I accidentally modeled it with units of kilometers. I am trying to scale the model down to its actual size but when I set the correct dimensions, something very odd happens.

This is what the model looks like at kilometer scale

When I set the correct dimensions for the object, it looks like this

The (very tiny) model is correctly displayed but it is hidden inside of this strange circular object, which is about .5 km in diameter. I am not sure what is causing this extra mass to appear outside of the correctly displayed model.

Ensure the object has a scale of 1, in object mode select your object and Ctrl+A / scale
Does your model have any modifiers ? If so you may need to adjust the modifier settings

There is a subsurf modifier on the mesh but I don’t think that’s the issue. This is what the settings look like:

This is what the correctly-dimensioned model looks like without the subsurf modifier:

I don’t think it’s the modifier, and the scale settings appears to be correct. I am at a loss here and since this is the first model I have put real effort into, I am quite frustrated at the situation. Any help would be appreciated.