Talos
I've never used "zipper" initiative, but I'm familiar with it and I can see its potential value. Though I doubt I will ever use it.
When playing online, I stick with initiative being re-rolled every round because it's automatic and doesn't slow the game down, at all. I prefer it because it captures a bit of the unpredictable, frenetic aspect of combat. Also, it can create some extremely tense moments when the dice gods allow all the monsters to go at the end of a round and then the all the monsters take their turn again at the start of the following round. The bad guys effectively getting a
Time Walk (MTG reference) is brutal but, on the flipside, it feels awesome when it happens for the group.
As far as keeping 5e combat fast-paced and engaging....that's extremely challenging because 5e is inherently fairly slow.
The most impactful suggestion I can give you is to be strict with players in regard to them knowing what they plan to do with their turn. If each player spends 2...3..or 5 minutes figuring out what they're going to do, a single round of combat can last a half hour. My players have 30 seconds to tell me what they're going to do. Otherwise they take the Dodge action and pass. There's some leeway if the player has pertinent questions or the situation is complicated and/or needs clarification. It doesn't take getting skipped many times before people figure it out.
Admittedly, paying attention can be tough for people because 5e isn't great at holding a player's attention when it's not the their turn. I've tried to help mitigate that flaw by introducing quite a few additional sources of Reactions (magic items, additional abilities, new spells, etc.). Players who pay attention can use the new tools to capitalize on openings during other people's turns. Though, to be fair, it requires a fair amount of work to create, balance, and implement those things.
P.S.
Awhile back I had a couple guys ask me to post my houserules file, which, at this point, has blossomed into an almost DC20-type-thing. My game is still definitely 5e, but I've created and scraped my hundreds of books for the version of each mechanic that best suites the style of game that I want to run/play. Anyway, the formatting wasn't fit for public consumption, but I am actively working on polishing it so I can share it with the few of you that were interested.