I'm with you here. Combat is tedious and often boring. Some of the best, most memorable times are from moral conundrums that fit within the issues of the OP. Like when the PCs found, at the end of a dungeon, three baby goblins left behind by their recently slain parents.

After two years of that ongoing campaign, the town they live in now has a toddler goblin being raised in disguise by the half-orc who runs waste management services, and a wyrmling red dragon whose father was too often away burning villages to have imprinted his evil ways; Littletooth stays busy keeping the cooking fires and forges at optimal temperature, and minding his horde of graciously donated copper coins.

There was a pit fiend trapped in a magic circle for ten thousand years, his life force being sapped to power a massive magical dam. Our cleric found the devil was ready to atone for his sins, and now serves the cleric's goddess among the stars. The goddess was pretty stoked to show off her pit fiend acolyte to the other good gods. During downtime a gnome party member called in his extended family of eccentric inventors and engineers to revamp the legendary dam to just work like a normal fucking dam.