I tend to see game mastering as management. If players behave in a way that prevents fun, there is probably something the game master does that unintentionally feeds the situation. So I think you’re looking at your situation the right way. Here are some thoughts.
The possibility of Defeat, role playing’s best friend. Players tend to willingly role play if it’s necessary to achieve their goals. Often however, game masters defeat themselves by providing simple goals and easily defeated opponents not requiring planning, tactics, or role play – so players simply role dice. It is extremely common, even in store bought adventures, for every monster/s that PC’s might encounter to be 75% as strong as the party. Players merely need to not screw up or suffer terrible luck to prevail. To solve this, provide opponents that are stronger than the party, so strong they can’t be defeated in toe to toe battle. Now players need to THINK of a better way. Here’s an example.
While traveling, 3rd level PC’s encounter a giant raiding a village. The giant is drunk, having broken into a brewery. For now, the giant is content to drink his fill as the villagers stand around wondering what to do. Even in its drunken state, the party can’t hope to defeat the giant in open combat. But if they can organize the villagers with a clever strategy, then victory becomes possible. How? Through role play.
Situations over Combats: The problem with a lot of ‘random encounters’ is that they are actually ‘random combats.’ Once combat begins, conversation is off the table. Particularly if all the monsters want from the players is for the players to die. Combats are like – two men enter, one man leave. What’s to discuss? Situations on the other hand are complicated requiring brain power (either strategy or role playing) to resolve. In encounter form, situations will often appear as stalemates that players most resolve to win. More importantly they must make decisions. Here’s an example.
5th level PC’s encounter a tribe of orcs preparing an attack on another tribe. Which side do they choose? Do they stay loyal to the group they joined? Does that tribe remain loyal to the PC’s? Much of the role playing will grow from the PC’s deciding what they want to do, but also negotiating with the possible allies.
3+ sided combats: Far more interesting than two men enter, one man leaves is – three men enter, one man leaves. Many game masters play for years and devise hundreds of combats, but in every case its group A versus group B. Conflict is a foregone conclusion and the dice decide who wins. But insert a third party opponent and everything becomes more interesting. On some level, for some period of time, an alliance must be formed, hence the role play. In story telling this is standard dramatic structure, like the classic love triangle: two guys, one girl - much more interesting than one guy, one girl.
Flat, Bright, and Empty: Many game worlds, if you think about it, are unnaturally devoid of detail most of the time. When encounters occur, players have almost no information about the world around them to guide their thinking. Combats occur on flat ground, with good visibility, devoid of obstacles – flat, bright, and empty. In the real world, this only occurs inside a boxing ring in order to keep everything fair and balanced between the two opponents. Thus, there’s nothing to do but get to fighting. Battles are the opposite. They occur on uneven ground in difficult situations. Military tacticians seek to use the inequalities of environment to their advantage (control of the high ground, superior cover, etc.) Essentially the idea is to cheat the situation so that your side has more advantages than the other. Thinking up these ways to cheat will drive role playing.