I have not used a .410, but the heavyshot that they have out now is amazing. We have been using it for a couple of years. I shot a jake last year at 40 yards with my son's 20 gauge and it about took it's head off. It drove it straight backwards and flipped the bird over. It barely twitched after that. The Federal shells that we are using are no longer made, but I will be buying these when we need more as they replaced them. We were using 7.5 in the 20, but they make #9 shot for the .410 and the 20. You getter better penetration with this heavyshot with #9 than you do with #5 lead. The fact that you have so many more pellets with the smaller size the pattern is alot better at longer ranges. People are killing gobblers at 50 yards with a 20 gauge. I probably wouldn't be afraid of 30 yards with a .410. It may seem like I am bragging these up, but I honestly could not believe the results.
https://www.federalpremium.com/products/shotshell/premium-turkey/heavyweight-tss
The other thing is my girls actually started hunting turkeys with a crossbow instead of a shotgun as they liked the crossbow better. It is great if you have a blind to hunt out of. Obviously run and gun it isn't nearly as good.
As a 3rd option you might even want to consider a 20 gauge. A semi in a 20 doesn't have alot of recoil. You can always just put in 1 shell at a time till she gets more experience.