Alright, where to start... First of all, I agree with MattR; one patrol does not constitute an SPL. However, being NYLT trained myself, I can say that if she has not shown interest in actually leading, then she isn't actually leading, and therefore she is not in fact a quality candidate for an SPL position.
I would also inquire as to the activities your troop does for both meetings and campouts. If there are no scout related games at meetings, no EDGEing happening on campouts, or perhaps, as happens in a lot of troops including mine, they're on their phones instead of scouting around, then I would suggest doing a constructively competitive activity, such as bowling, pioneering stuff, and (my personal favorite) Capture the Flag.
In terms of recruiting, instead of social media, like her vision, your troop might consider (if you're not already doing so) using recruiting campouts to bring cub scouts in. Pick a local place with plenty of space for things like a monkey bridge, tomahawk throwing, an axe yard, fire building competitions, and scavenger hunts. These activities show how much fun camping in the Boy Scout program can be. This in turn makes them interested in joining and wa la, five becomes ten, ten becomes twenty, and before you know it, you have a fully functioning troop! Other than that, visiting pack meetings is also a great idea. You can also perform uniform inspections there, as something to do. Just have a committee member contact the pack and arrange a day for it.
To conclude this informative rant, I wish you luck, and may your troop grow ever larger.
Yours in Scouting, The Green Wizard