One option could be to ditch the standard DND combat in favour of skill challenges. The party has to get X successes to win or Y failures to lose, both of which are tracked by a clock. You can also get rid of the standard initiative and have it so enemies act on player failure or as opposition to their actions. Alternatively the bad guys can have a clock of their own up to you. Now this will mean that you'll have to figure out ruling for purely damaging spells. Maybe they help with checks?

There are many games that do rp well and manage the combat just fine. Obviously this one is my favorite https://fateofdungeons.com/what-is-fate-of-dungeons/ However all of the pbta are super rad for this too. My key observations are a system tells you what it is about with its rules. Games with mechanics for making difficult rp choices that drive the story and the action are really fun. Msg me if you want the rules from that link.

Could always get into a game called blue rose. Did a flip through of core rule book on my YouTube channel