I have to admit that Laverly has a “made up” feel to me, like the first part of [name]Laverne[/name] with an -ly added to the end, but I do like the flow of Laverly [name]Kate[/name].
Natelyn feels too “made up” to me (but that’s just me), like the boy’s name [name]Nate[/name] with the trendy -lyn ending tacked onto the end (and it also reminds me of the trendy [name]Katelyn[/name]), but if you love it, that’s what matters!
I guess I’m thinking that with Varsity, you found an actual word as a name, so I think it would be cool for your next baby girl to have a name as real and distinctive as Varsity, if that made any sense. 
[name]Do[/name] you like either [name]Natasha[/name] (not very distinctive, though), [name]Natalia[/name], or [name]Natanielle[/name]?
I forgot about the boys’ names! You liked [name]Kyle[/name], [name]David[/name], and [name]Gabriel[/name], and I think that they’re great names. Out of the three, [name]Gabriel[/name] and [name]David[/name] are my favorites.
[name]David[/name] [name]Alexander[/name]
[name]David[/name] [name]Benjamin[/name]
[name]David[/name] [name]Charles[/name]
[name]David[/name] [name]Elliot[/name]
[name]David[/name] [name]Harrison[/name]
[name]David[/name] [name]Miles[/name]
[name]David[/name] [name]Maxwell[/name]
[name]David[/name] [name]Samuel[/name]
[name]Gabriel[/name] [name]Dexter[/name]
[name]Gabriel[/name] [name]Edward[/name]
[name]Gabriel[/name] [name]Isaac[/name]
[name]Gabriel[/name] [name]Jude[/name]
[name]Gabriel[/name] [name]Joseph[/name]
[name]Gabriel[/name] [name]Pierce[/name]
[name]Gabriel[/name] [name]Simon[/name]
[name]Gabriel[/name] [name]Thomas[/name]
[name]Gabriel[/name] [name]Vaughn[/name]
[name]Kyle[/name] [name]Benjamin[/name]
[name]Kyle[/name] [name]Donovan[/name]
[name]Kyle[/name] [name]Everett[/name]
[name]Kyle[/name] [name]Harrison[/name]
[name]Kyle[/name] [name]Jameson[/name]
[name]Kyle[/name] [name]William[/name]
[name]Kyle[/name] [name]Xavier[/name]
(I forget your sons’ middle names, so I aplogized if I used one of their middle names as a middle here!)
Good luck! 