Considering giving this initiative system a go with a few tweaks:
1)I think I like the Weapon Speed and Spell Disruption variants. Giving some utility to lower-damage weapons is appealing to me. You could even give some weapons a "fast" quality that they roll an initiative die lower than what their damage die suggests, or "slow" to do the opposite.
2)I think I might tweak the delaying rules to allow for actions on another character's turn, so long as they can describe what they are waiting for, and can roll low enough on initiative to do it. For example, if two orcs with bows are moving, firing, and then moving back behind full cover, and a player with a bow rolls low on initiative, he could declare that he is going to fire his bow at an orc if it comes into sight. I don't think this would necessarily break anything. However, readied actions wouldn't be able to fall over to the next round under this system.
3)An alternate delaying system... another tweak I might allow is allow players to "wait". Essentially the player does not roll initiative until he is ready to declare an action. Once the player declares an action, he rolls, and adds the current initiative count to his roll. For example, The cleric is unsure of what to do with his turn, so he waits. On initiative count 5 the fighter is attacked and wounded. The cleric announces he wants to move and cast a spell, so rolls 1d10+1d6 and adds it to the current count (5) and rolls an 8. He will act on initiative count 13. This seems fair to me since the cleric got information he could not have had otherwise.
4)Redeclaration: If a player's turn comes up and wants to declare a different action than the one he declared earlier (for example, the melee fighter's turn comes up and there is nobody for him to attack, and he didn't declare a move) then instead of taking any actions he declares a new set of actions, rolls the dice, and adds them to his current initiative count. You must roll all dice for the new declared action(s.)
Example: Regdar declares a melee attack, and rolls 1d8, and rolls an 8. On initiative count 6, his allies fell the enemies that were adjacent to Regdar. Regdar curses and wishes he had declared a move, but he has to wait until his turn to redeclare. On initiative count 8, it's his turn. He redeclares a move and a melee attack, rolling 1d8+1d6 and gets a 4. On initiative count 12 Regdar will gather his wits and move to a new foe and attack.
I think this is fair as well, since *not* declaring a move is a sort of gamble, and having a late initiative is probably enough of a penalty by itself without robbing the player of his turn as well.
5) I will probably not have bonus actions count against initiative. However that leaves an issue where if a player chooses to ONLY use a bonus action on his turn (no move, no attack, no anything, just a bonus action) he has no dice to roll. You could rule that such a player would act on initiative count 0 (unless he was surprised) which would be... interesting? Possibly game breaking?