Do NOT get anything with a big loop.
Shooting a lever gun fast means trimming away any risk of lost movement in the fingers. And that means you want only enough room for the fingers and no more than that. In fact a big function of the usual padding added to a lot of CAS rifle levers is to remove the lost travel as much as to reduce the bruising on the back of the lever fingers. With the idea that as much as possible of the finger movement should move the lever any sort of big loop is going to be a significant disadvantage.
If you go for Henry I'd say go with the basic H001 model with the round barrel. That round barrel is a lot lighter than any of their octagonal barrels. That makes the front weight a lot less and for a youth to hold up so she can focus on fast and accurate shooting.
The shoulder stock will be too long of course, unless she is quite tall, But any smith or even yourself if handy with tools could cut it down and install a new butt plate to suit her. And keep the piece that came off to put back on at a later time.
The new butt plate can be made from any hardwood. It's only there to save the edges of the cut off stock for later when you add back the cut off piece anyway. And wood will be fine because to help with a steady hold to the shoulder the usual fix is to add a butt cover of leather that has the butt end as the flesh side of the leather. And often that flesh out rear piece is laced with leather lacing to the side wrap around. The leather lacing again helping to get a more stable hold just that much more than the flesh out end cap. And that leather butt cover protects the temporary wood butt cap just fine.
I use my own Henry H001 for some rapid fire fun in the local speed steel matches. I even manage to beat the odd semi. Even shot quickly it never fails. And it lasts for a long time between cleanings. Like up around 10K or so.
For a shotgun the only pumps allowed under the current rule book are Winchester 1897's. And I'm pretty sure those don't come as .410's. The following is in the rule book for Buckaroo....
Side-by-side, single shot, and lever action centerfire shotguns in .410 caliber and
28 or 32 gauge are allowed within the Buckaroo Category only
I notice it says that lever action shotguns are allowed but the only one I find is the big frame and heavier Henry. Plus being a lever doesn't help much since none of the shotguns can have more than two rounds at any time in them. So the usual option is either a slick working single barrel with an ejector or a side by side.
From a quick bit of checking it appears that the Scout is a smaller frame than the full size 1873. If so then a good companion if you can't find another Scout would be a Uberti Stallion which is also a smaller frame and likely on par with the Scout. If her hands are really small and even the Scout is a big fit for her than have a look into the Ruger Bearcat. It's quite a bit smaller than even the Stallion and likely the Scout.
