I think this version of the Soul Burial works out better:
Soul Burial (Su): A Shinigami who is adjacent to an undead or a creature with the Spirit subtype may attempt, as a full-round action, to release the spirit to the heavens. The Shinigami must make a diplomacy check against a DC equal to 10 + the creature's HD + the creature's Wisdom modifier. Hostile creatures receive a +8 bonus on this check, unfriendly creatures receive a +4 bonus on this check, and indifferent creatures receive a +2 bonus on this check. Mindless undead do not get this check; they are simply destroyed, their spirit released to the heavens.
An undead destroyed in this manner can be raised as though it were never undead, provided the spirit is willing.
I also agree about their Spirit Weapon needing to be... better. I'd go with the Samurai as a basis for what to work with. It still gets Ghost Touch for free, but the Shinigami can imbue it with m0r3 p0w3r. You could charge them a small amount of experience points or gold to get special abilities, but I'm thinking an enhancement bonus ought to come at a level progression (+1 at first, +2 at fourth, +3 at eighth, +4 at twelfth, and +5 at sixteenth).

Methinketh you'd be well-served to change the Undead Slayer to a progression. +2 vs undead at 5th, +4 at 10th, +6 at 15th, +8 at 20th, and so on a la Ranger. Either that, or evil outsiders with the Spirit subtype. Depends on what you want to call Hollows.

I disagree with Innis; unless you want to make a PrC (or say Kido users are multiclass casters), leave the spellcasting progression in. Then again, I don't know ToB maneuvers at all so I'm biased against them to begin with.

... I see nothing wrong with diverging from the source material to give them wings.