A Smart Object is an embedded document, so any Layer Comps within it are accessible only when that document is open.
The best solution, from your description of the problem, would be to create a separate Smart Object for each layer comp. Using
Layer comps to files from within the Smart Object and Placing each of these in the main image is probably the quickest way to get there, then associate each placed object with the appropriate Layer Comp in the parent.
For future projects where this kind of situation is going to obtain, create the first SO in the usual way, then create as many additional ones as you need using
Layer > Smart Objects > New Smart Object via Copy to give yourself independent objects. (You can't just copy, because then all instances stay synchronized and a change to one would be replicated in all the others.)
[Added after clarification of the problem]
Filters are a different issue entirely. The simplest approach to replicating filter settings (if it's just one filter) would be to create an action that drops down one layer, makes it visible, applies the last filter settings (as in Cmd-F/Ctrl-F) then hides it again. You would apply the filter to the top object in the set then run the action. Assign it to a keyboard shortcut.
If this scenario is one you run into frequently, you can script it to make it more flexible.