Doing Initiative Like a (Dungeon) Boss!

Okay, so I've been playing this fun RPG batttle game on my mobile phone called Dungeon Boss.  You acquire heroes, run dungeons, level up, etc.  The initiative is based on classing each hero or monster as fast, normal, or slow.  Fast characters/monsters go first, then normals, then slows.  I'm interested in adapting this for regular RPG games.  I don't quite like the old school "party initiative" because it lumps everyone together regardless of dexterity, encumbrance, etc. and I'm tired of slogging through the stilted 3E/Pathfinder individual initiative (even though I generally treat the party's opponents as one group to speed things up).

So the Dungeon Boss initiative model looked like an interesting alternative.  The first step is to sort your classes into the three speed categories:

Old School Classes
Thief = fast
Halfling = fast
Fighter =normal
Elf = normal
Magic-User = slow
Cleric = slow
Dwarf = slow


D&D 3E/Pathfinder Classes
Fast:
Barbarian
Monk
Rogue 
Normal:
Bard
Drud
Fighter
Paladin
Range
Slow:
Cleric
Sorceror
Wizard

If one side has more fast heroes than the other then that side automatically gets the initiative.  Otherwise, you roll 1d6 for each side as though you were doing party style initiative and the higher scoring side gets the initiative  The winning initiative side acts with all fast heroes then the other side acts with all its fast heroes.  Next all the normal speed heroes on the winning side act, etc.  The overall sequence will look like this:

1. Winning side fast heroes
2. Other side fast heroes
3. Winning side normal heroes
4. Other side normal heroes
5. Winning side slow heroes
6. Other side slow heroes

This method has its own quirks but I'm looking for something with more granularity than old school initiative but without the tedious fiddly bits in 3E initiative.