Maidhc O Casain
Na Bith Mo Riocht Tá!
Halal will (eventually) be very focused on initiative, so my concern (which you addressed, pm) would be only that whatever method we do doesn't detract from that usefulness - class features, feats and traits to boost it become a much harder investment in that case.
Averaging initiative (without some arrangements for such characters) 'waters down' the advantage of taking Improved Initiative (and other feats and traits that allow one to act more quickly) as well as that of adding Wisdom mod to initiative roll (which Halal will do at second level).
Another possibility would be to just do initiative in order of highest modifier to lowest without rolling any dice at all (tie goes to the higher DEX, still tied is GM choice).
Averaging initiative (without some arrangements for such characters) 'waters down' the advantage of taking Improved Initiative (and other feats and traits that allow one to act more quickly) as well as that of adding Wisdom mod to initiative roll (which Halal will do at second level).
Another possibility would be to just do initiative in order of highest modifier to lowest without rolling any dice at all (tie goes to the higher DEX, still tied is GM choice).