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Don't use scenes. Use movieclips.
To expand on what ClayUUID said, each movieclip can have 16000 frames, so if you had each of your sub-FLAs in its own movieclip, taking only one frame of the main timeline each, your navigation page would go to that movieclip in much the same way you were planning on going to a different scene.
All of the code at the main timeline of each FLA would be moved to the timeline of its movieclip in the combined FLA. If you're using external AS3 classes, you would take the document class of one FLA, and in the library of the combined FLA you would set the base class of the movieclip for the dedicated movieclip you have made to that same external AS file.
That works great!
Thanks for pointing me in the right direction, and explaining it enough for this newbie to understand.
Thank you for your help.