Leslie:
WOW! Bouguereau in miniature! You did an admirable job especially considering the size.
I did some study of miniature portraits before I went to Charleston, South Carolina where they have a museum with a miniature portrait collection.
The collection was unbelievably detailed and just lovely stuff. Most were painted on ivory.
This is a very interesting course of study if you decide to pursue it further. As to keeping your paint layer smooth, you need to work with a medium that levels the strokes, and you can very very lightly sand (yes, sand) your piece between coats to take off any proud spots or strokes that stand up too much. Use a wet sandpaper that is good for automotive - 600 grit. Again, you will want to be careful not to sand too deep, but it will help to keep your surface quite smooth.
As for a surface to paint miniatures on, may I recommend ABS plastic (yes, I said ABS plastic). Sunlight is the only thing that kills it - cover it with paint and you are good for 1000 years. If you get it at about 1/6 inch thickness, and then sand the shiny side to remove the gloss, you will get a surface that is a lot like ivory. Since ABS is microporous, oils will stick with no problem, and your sanding the surface will further help by creating a mechanical bond.
Good luck and a real nice beginning!