I go to Dharma for my dyes too. They have a huge selection of pre-mixed colors in the Procion dyes. I don't use Rit and have no info about how it works. If you use the Procion dyes, you should check to see what the tee is made of. If it's 100% cotton, the procion dye will dye pretty true to color, but if its a 50/50 cotton/poly blend, the polyester won't take the dye like the cotton does so you'll get more of a heathered look.
Dharma ships very quickly too. You can check out their colors on their website. They have a bunch of different purples, so I bet you could find what you are looking for. As far as the shirts you have, without seeing them, Idk if I'd try dyeing over them or not. There is a color remover that you can get, but I've never used it. And I'd worry that, just like with bleach, you could lose some of the wear strength in the fabric. you know?
Sorry I don't know anything about Rit, but for dyes (and almost anything textile), Dharma is THE place. I hope this at least helped you some. Good luck with your project!