Let's mess with initiative!

I have a complicated relationship with combat in D&D. Hooray — so dramatic! Oh no — so rigid! I've been thinking of some ways to decouple combat from its structure, hopefully making it more interesting. Let's roll initiative!

Goals

The two areas I'd like to improve with this little experiment are a) increasing drama and b) reducing mental load. The start of combat is very dramatic beat followed by some initiative bookkeeping, so that's my focus. I want to minimize the initiative process so it doesn't cause such a speedbump in the table's energy or the trailing duty of tracking it.

Option 1: The Line

Method: DM rolls once for all enemies together. This number represents the line. Players roll initiative normally and land either above or below the line. Then we proceed like this: above > the line > below.

Pros: Good for big groups. Freedom in turn order for players. Less trailing bookkeeping throughout combat.

Cons: Still undramatic. Still initial bookkeeping.

Option 2: Phoenix Cards

Method: I've seen Satine Phoenix talk about using this method to reduce the game's math load. She writes each player character and enemy on a blank card and draws randomly.

Pros: High variance (plus options to reshuffle for shenanigans.) Low initial bookkeeping. 

Cons: Doesn't account for individual initiative bonuses.

Option 3: Preroll

Method: Everybody roll initiative once at the start of the game. This number is each character's initiative for the entire session. DM pregenerates enemy initiative scores.

Pros: Opportunity for more planned player strategy. Zero initial bookkeeping. 

Cons: Doesn't reduce trailing bookkeeping by much.

Option 4: Wildcard?

Are there any systems that don’t use initiative in combat? I’ve seen a lot of people suggesting things like rerolling every round, or the Greyhawk system, but I want to see how hand-off we can get with initiative and keep it functional. Open to suggestions. Give me something exciting.