When you would've given a whole round out to the side with surprise, just give out one turn to the character with the highest initiative bonus on the surprising side (or just have the party elect someone). Then, roll initiative (you can keep 2024's advantage/disadvantage if you like, too) and go normally.
Makes ambushes worth getting (an extra sneak attack or TWF + hunter's mark turn is nothing to sniff at!), but means we're not going through EVERYONE before the other side gets to act. Which, even just as a meta-consideration, can be kind of tedious.
I like ambush being a potent strategy, I don't mind a significant advantage, I don't even mind the occasional binary result (I mean, you could use that surprise turn to teleport everyone to the next zip code, I suppose!), but I also try to avoid rolling dice when there's a foregone conclusion, too.