Based on your other girls’ middle names, I quite like [name_u]Evelyn[/name_u] [name_u]June[/name_u]. Actually, it’s my favorite without any context too. Other ideas:
[name_u]Evelyn[/name_u] [name_f]Isle[/name_f] (inspired by [name_f]Eileen[/name_f], but one syllable to match your other middles)
[name_u]Evelyn[/name_u] [name_f]Jade[/name_f] (similar to [name_f]Jane[/name_f], [name_u]James[/name_u], [name_u]Jay[/name_u]…)
[name_u]Evelyn[/name_u] [name_f]Janelle[/name_f] (combining sounds from your other middles)
[name_u]Evelyn[/name_u] [name_u]Jean[/name_u] (same as [name_f]Jade[/name_f])
[name_u]Evelyn[/name_u] [name_f]Jemma[/name_f] (a nod to your husband’s middle name)
[name_u]Evelyn[/name_u] [name_u]Wren[/name_u]
[name_f]Sylvia[/name_f]/[name_f]Silvia[/name_f], [name_u]Vivian[/name_u], and [name_u]Evelyn[/name_u] is my absolute favorite three-sister combo! [name_f]Violet[/name_f] is the perfect fourth name I love how they’re all six letters, and have that “v” sound, in different places. [name_m]Just[/name_m] thought I’d throw that out there
I like [name_u]Evelyn[/name_u] [name_u]Jean[/name_u], another [name_u]Berry[/name_u]'s suggestion a lot, but I also like [name_u]Evelyn[/name_u] [name_u]June[/name_u]. [name_u]Evelyn[/name_u] [name_f]Ivy[/name_f] and [name_u]Evelyn[/name_u] [name_f]Isle[/name_f] are also really pretty, but I like the trend of one-syllable middles and the L/J/L/J pattern.
I like the sound of [name_u]James[/name_u] the best, and I like that it honors her dad since the other girls all honor their mom/mom’s side of the family.
I love [name_u]Evelyn[/name_u] [name_f]Ivy[/name_f] however I voted for [name_u]Evelyn[/name_u] [name_u]June[/name_u] because you said that you loved the idea of their names having a connection which I also love.