I'd be inclined to try a mixture of cerulean blue with a navy that's
been corrected for greenness by the addition of a bit of red MX-5B,
such as Dharma's Strong Navy or Jacquard's Navy 078. They are
navy blue MX-3R, but another navy dye, cobalt blue (blue MX-2G),
ought to work, as well, with a touch of red MX-5B to reduce the
greenness of the 'cobalt' and the cerulean blue for added brightness.
Or a large amount of blue MX-R (which Dharma calls "sky blue",
but it's more of a royal navy if you use enough of it) with a bit of
cerulean for brightness.
Interesting: I just saw this morning that Jacquard Products is
now selling an indigo dye kit "for ages 5 and up":

No need for lye since it's pre-reduced indigo. Age five seems
a little low even so.
Paula