A few thoughts:
1. Instead of having movement be just a die roll (which still leaves "mini-teleport" movement), why not just have it take 1 segment to get started and then be 1 more segment per x-distance moved? I say x-distance rather than a set number of feet because in an open field situation one will be able to move much farther in a given time than in a tight crowded passage. This also tells the DM where you're going to be when while you are moving on a seg.-by-seg. basis in case you run into something like a spell's area, or draw an AoO, or whatever.
2. Multiple attacks really should get separate initiatives. A simple way to do this would be to just roll as normal (so, d8 for melee) twice, and have the attacks happen then - one on a 2, say, and one on a 6. Maybe add in that the rolls cannot be the same; reroll one if they are.
3. To tone down the Ranged stuff a bit - sure they can be fast on the initiative but there need to be much more severe penalties for shooting into melee, and even more severe penalties for shooting
while in melee.
4. I'd tweak the caster roll to be d6 + spell level; and have it interruptable (and the caster lose all Dex bonus to AC) between the original initiative roll and resolution. Example: caster wants to chuck a fireball, 3rd-level spell. She rolls 2 on her initiative, so that's when she starts casting; to resolve on a 5. If she's attacked on a 1 she gets her full defenses. On 2-4 she doesn't, as she's concentrating on her spell and the handwaving required. On 5 she resolves, after which she's back to normal again till next round. And if she's interrupted - well, that's where the wild magic table comes in handy.
5. For simplicity's sake I'd put in a blanket rule that spells always resolve at the [start/end, pick one] of the segment, to avoid headaches around - for example - whether the fireballed goblins acting on a 5 got their shots away or not.
6. To avoid or at least mitigate Delay abuses, put a randomizer - say, d3 - into how quickly a delayed action can happen after its trigger occurs. And if you delay until after the last action taken* in a round (because your triggering action didn't happen) you've delayed right off the round's end and can roll afresh for next round.
* - unless that last action is what you specified at declaration as your triggering action, in which case you go next.
Lan-"there's simpler ways to do this, but Mearls is certainly on the right track"-efan