Good that you specified the Tints of Nature semi-permanent, as the permanent version is definitely not PPD free, and the same goes for Naturtint! (The latter doesn't have a semi-permanent version, to my knowledge?)
Tints of Nature and Naturtint at least are honest about their permanent dyes containing (what they call low levels) of PPD, but it's really annoying how many dyes are advertised as "PPD free" altogether, when they do contain loads of PPD derivatives, even if not the actual paraphenylene-diamine, and those have basically the same effects...! Talking about misleading advertising... For example, this Apivita dye http://www.apivita.com/hair/hair-colorants.html is advertised as totally PPD free, but e.g. shade 7.4 has the following PPD derivatives (aminophenols): 2-Amino-3-Hydroxypyridine, 4-Amino-2-Hydroxytoluene, Toluene-2,5-Diamine Sulfate, p-Methylaminophenol Sulfate.
Those semi-permanent ones you mentioned are to my knowledge safe to use, but imo very expensive, especially in the long run; but if you can get them at an affordable price, go ahead
There are actually some other deposit-only dyes that are fully PPD free, and they come cheaper as well, like Adore, Via Naturals and Manic Panic. And burgundy red is one of the shades most do have (it's the more natural shades that can be harder to find), so they sound like perfect match for you
http://www.creativeimagesystems.com/...d=48&Itemid=60, http://texasbeautysupplies.com/via901.html, http://www.manicpanic.com (you can find more info and places to buy them by googling.)
And as for dangers of PPD, this makes a chilling reading: http://www.organicconsumers.org/body...olor102804.cfm Not to mention the sudden deaths or serious acute allergic reactions caused by hair dyes...
I decided to ditch PPD dyes too a few months ago, it's just not worth the risk (especially since I've used a huge amount of them in my life until now), especially as there are alternatives...
(Oh, and I think this would actually belong in the conventional products forum, as that's what these are after all, not herbal dyes )