Har! Seans23's PC was reincarnated in my campaign. He got reincarnated under extremely unique circumstances. When I designed his reincarnation table I was doing it with an eye toward several special influences: fey, enlargement, and mild demonic presence. If you know the WotC adventure series, then you can probably guess the circumstances: location, solar day, and in particular the reincarnatress. So his table looked like this:
01-12 centaur, 13-24 grugach, 25-39 half-ogre, 40-51 hobgoblin, 52-63 human, 64 ogre, 65-76 satyr, 77-88 tallfellow, 89-00 tiefling.
Sadly, he got the hobgoblin, which was I think the least interesting possibility, but as a monk he friggin loves it, as far as I can tell. I only included hobgoblin because it's the goblinoid missing from the regular reincarnation list. {If he had gotten human in this case I would have reset him to the beginning of his current level and not docked him one.}
Note that they are all rather large bodies, to incorporate the enlargement variable. Note the heavy fey influence, and that even the sole Small body on the list is the "large" halfling. If I were to redesign the list, I'm not sure I would keep the half-ogre (or at least as a 15% possibility) because I have realized that it's a +2 LA, not a +1 LA as written in, um, CW or SS or wherever it is listed. Be careful about including really powerful possibilities. As I said, the circumstances were truly unique, and even if the party tried to duplicate the experience, they would get a slightly altered (and weaker) list.
But I also have ideas for other reincarnation lists, such as ones in subterranean vaults of evil, or on other planes, or with bizarre material components. The trick is to only use the special list if the circumstances demand it, like if he were being reincarnated in the runoff from an evil temple's blood altar, during the new moon, by the half-cousin of Asmodeus. Or something like that. Keep the specialized lists...special.
You can also do some Rule-0 tweaking, as Seans23 did during my PC's recent (second) reincarnation. {We are each other's DMs} My PC was a high elf, then reincarnated as a half-orc, then reincarnated as a halfling. Because of unique circumstances (lead druid of his circle, summer double-solstice, druid was "trying" to get elf), Seans23 tweaked halfling into tallfellow. This fit just fine, and no one complained (especially me).
In the particular case of the phoenix helm, I would possibly add some air/bird influence to the table, such as raptoran (though I find them annoying). If it's a true phoenix thing you're going for (fire bird and all that), then add some fire to the table, like half-elemental, though maybe those are too powerful; I don't have the stats in front of me, so I don't know about the LA. Remember to try and parallel the existing reincarnate table, with mostly monstrous humanoids and a few humanoids sprinkled in. And one rather decent 1% possibility, such as I had with ogre in the above table. Heck, the 1% on your table could be half-avoral or something!
Recall that in his new form he won't get any new racial HD or skill points, so sometimes the LA might even be lower. I don't charge Seans23 for the hobgoblin's LA for this reason. Just keep the LAs low, as he will not lose/gain the racial hit dice from being born a minotaur.
