Collecting with a snaffle?

My horse is currently being ridden in a french link eggbutt snaffle. She is a strong horse, so it's difficult to ride in the snaffle, but I'm doing it anyways. Whenever I rode her in the shank, she would go on the bit and collect beautifully. It was true collection, she wasn't hollowing her back. Anyways, now that I have her in the snaffle, I can't get her to collect. Whenever I ask, she sticks her nose straight out and tries to evade the bit. She will throw her head as well. How can I get her to collect? Should I try a running martingale? What about a flash noseband? Different bit? I would keep riding her in the shank, but I ride her English too, so I switched to a bit that I can use for both.