Although I've experimented with the alternative initiative rules in the DMG and with other ideas I've read about online, I always return to the standard initiative rules in 5e combined with initiative tents draped over my DM screen for tracking order. The players understand it, it's straightforward, and it works, although I usually have to call out names to keep things moving smoothly.
Sometimes when the players are exploring a dungeon I will have them take their turns in seating order instead. Thus, play proceeds in a clockwise rotation around the table starting with an arbitrary player, usually the player at the front of the conga line or the first player through the entrance. When play reaches me in the rotation, I will take any ally, monster, or lair actions that should arise. Players seem to prefer seating-ordered initiative, probably because it is a familiar mechanic in board games. They feel more confident taking their turns right away without waiting for me to call names, and it speeds play quite a bit.
However, any game features that depend upon going first in combat (such as the assassin rogue's Assassinate feature or the doppleganger monster's Ambusher and Surprise Attack features) or game features that affect initiative rolls (such as the bard's Jack of All Trades bonus or the UA revised ranger's advantage on initiative rolls) are nerfed when we use seating-ordered initiative. It's also unclear who exactly I should start the rotation with and whether we should continue rotating for the whole dungeon or restart the initiative with a particular person whenever a threat appears.
What is an effective house-rule to use primarily seating-ordered initiative while preserving the utility of game features that depend on going first in combat or that influence initiative rolls? Answers should be based on experience, not conjecture. That is, I'm looking for a solution that proved to be objectively effective for whichever person employed it or experienced it at their game table. In addition, answers should not depend on altering the seating order of the players. Assume the seating order is arbitrary and fixed for the entire session.
Note that answers suggesting alternative methods for tracking standard initiative (whether they be tents, cards, placards, lists, or so on) do not actually answer the question I am asking. Correct answers to this question must establish a house-rule for calculating initiative in a non-standard fashion, not just for recording standard initiative using a different medium.