The Unearthed arcana article on the grayhawk style initiative system has been out a while. I've had time to let it roll around in my head. I think it's an interesting idea, I'm not totally against using it....but I'm not totally sold on it.
I think what really bothers me about it is lowest going first. It feels so counter intuitive. All of 5E is roll high. Maybe if I used it regularly I would I would get us to it.
My only analogy for how rolling low for initiative feels to me is if I was driving, and at every intersection there was a roundabout, and in roundabouts you drove in the opposite side of the road. You drive on the same side before the roundabout, same side after, but while in it, you drive in the opposite direction in the opposite lane.
After a lot of mulling it over I came up with what for me feels much more organic to 5E. Everyone rolls a D10 (D20 if you like but I feel d10 makes the bonuses more meaningful) highest roll goes first.
Ranged weapons, including bows, wands, cantrips and any other ranged fast attacks get a +6. Melee attack, fisticuffs, Molly whopping of any kind gets a +3. Spell casting is just a standard roll.
As a totally optional rule, for this totally optional rule: If player chooses to move after their action, no matter if the choose to shoot, Molly whop, or cast add +2. Moving before the action doesn't give a bonus or penalty.
What I like about this is it can be recorded on the character sheet. Add bonus for type + Dex adj.(if you choose to keep Dex bonus)= Initiative bonus. Long sword with a +2 Dex adj.? Then +5 to initiative.