Been done already in R/C soaring and free flight. Investigate spray can stencil ink. Spray your balsa parts lightly after cutting them out and before assembly. Glue will still penetrate the balsa, but use glue sparingly. Like you found out, everything has to be prefitted and sanded, or you sand the colors off. Not widely seen because of the extra work involved for what most perceive as an underwhelming effect.
  Type at you later,
  Dan McEntee

Does it run when you dope it?

No. At least I've never had it run.

On the low buck DIY side of things, I have used DesignMaster floral dye to tint both balsa and the adhesive side of clear lamination film. 
DesignMaster stuff is available at craft stores.  Michael's, ect.  Unfortunately, there are only a few colors that I would consider using.  https://dmcolor.com/explore/color-sprays/tintit-sprays/#&panel1-1

I would think you could also try using Higgins or a similar non-fading ink dissolved in clear dope, or possibly a bit of denatured alcohol.    https://www.higginsinks.com/dyeinks

TransTint is an amazing product, used extensively in the expensive guitar realm.

The Orange Chizler is Mike Haverly's plane. A flying buddy of Pete's. And mine.