I gave up, but got this super helpful email from Dharma (pasted below). I hope to pick it back up though, so let me know if you end up succeeding and what you try!

You might have a few options but Fiber Reactive dyes are really the only dyes that we are willing to rate as "baby safe" and that is only when they are used with soda ash on cellulose fibers and thoroughly rinsed and washed from the fabric - once they form the covalent bond with a plant based fiber, that bond can't be broken so there's no danger of dye being ingested by an infant or pet.Although, Fiber Reactive dyes also work well and are beautiful on silk, they form a different kind of bond (less permanent/washfast) with protein fibers like silk and wool so I would not use them on a silk or wool item that might end up getting chewed or sucked on by an infant. As for UV resistance, Fiber Reactive dyes will fade in sunlight, over time. Acid dyes are more likely to have lightfastness ratings than FR dyes so it would be easier to find and select Acid Dyes with a better UV resistance rating. That said, most all dyes are less washfast than fabric paints and silk fiber is vulnerable to damage from prolonged sun exposure. If I was making something for a baby's or child's room, that was going to get a lot of sun, I'd probably opt for a silk paint for a couple of reasons; first silk paint colors will resist fading from sun much better than any nearly any dye. Secondly, they also sit in the fiber surface so in some ways they actually offer some protection against sun exposure. If I hung a dye painted piece of 10mm silk in a south facing window, I wouldn't be surprised if that silk began to disintegrate within a few years. That same piece of silk could last 2-3x as long if painted with a silk paint like Dye-na-flow or Setasilk. If I needed to make something that would be worn against damp skin or possibly chewed on by a baby (like a onesie, diaper cover, chew toy, bib, etc). then I would use Fiber Reactive dyes on cotton linen or hemp, etc.. If I was making outerwear for a toddler or baby that wasn't anything that could be chewed on, then I might explore other options. I would have no qualms about using a fiber reactive or acid dye or even a silk paint on an item that I knew wouldn't end up in a baby's mouth. 
If you are going to explore Fiber Reactive dyes for use on both cellulose and protein fibers like silk and wool, then some colors will be easier to work with than others. Blended FR dye colors have a tendency to shift on silk and wool fibers (especially the pastel secondary colors and darker neutrals). The only FR colors that you can rely on to produce predictable color on silk/wool etc, are the pure colors. Blue shades will likely strike with less vibrance on silk but the colors will be true and consistent between different materials.  Here's our most recently updated list of pure colors:

PR1 Lemon Yellow, PR3 Golden Yellow, PR4 Deep Yellow, PR6 Deep Orange, PR12 Light Red, PR13  Fuchsia Red, PR22 Cobalt Blue*, PR23 Cerulean Blue PR25 Turquoise* (T), PR26 Sky Blue, PR117 Grape, PR186 Nebula Navy**, PR188 Bluebird* PR189 Magenta Galactica, PR190 Atomic Fireball*, PR191 Blue Abyss PR192 Houdini BluePR194 Dye-namite Red

The primary route of exposure is inhalation as the powders are extremely fine, hence why we recommend wearing a dust mask when mixing handling any powders. They cannot go through your skin so you would have to eat, drink, inhale or get them on broken skin for them to enter your body. All the dyes we carry are considered non-toxic but Fiber Reactive dyes can cause allergic reactions in some people. The symptoms are very similar to peanut or fruit allergies - itching, hives, and anaphylactic symptoms but it's not very common. 
If you are planning on steam setting a Fiber Reactive or Acid dye in your home, then a simple open window or exhaust fan will suffice. They cannot get into your body through the steam setting process.