Hi Debbie!
Thank you so much for your compliment on the panel! I'm glad you have found us helpful in planning your vacation.
In regards to your question - this is a tough one, and my honest opinion is that you will probably not make it on time to see Fantasmic from the beginning. Assuming that you get seated right at 7:20, I still think that dinner for a large party will take the better part of an hour if not longer. You would also have to factor in the time it takes to walk from Mama Melrose's to the amphitheater where Fantasmic is held.
I'm not sure when you are going on vacation, but during the busier summer months the amphitheater has been known to fill to capacity before the show begins leaving no available seats and standing room only at the back. During the slower season there is definitely a chance that you could show up right when the show begins or part way through the show and still find seats - although you may have trouble finding 16 together.
My suggestion would be to try to find earlier dinner reservations at Mama Melrose's. You can easily check to see if anything earlier is available or opens up by checking the online dining reservations system by following this link:
http://disneyworld.disney.go.com/parks/hollywood-studios/dining/mama-melroses-ristorante-italiano/ and clicking on "Make a Reservation".
If you aren't able to find an earlier dinner reservation, you could try to catch Fantasmic on a different night if possible. If all else fails, you could inform your server at Mama Melrose's that you are in a bit of hurry and they might be able to help move your meal along, but I would hate for you to have a rushed dining experience just to make it to the show on time.
I really hope you are able to make everything work out! Have a wonderful vacation!