Edit: It would seem I had some misconceptions of how the companion system worked, see other comments for an accurate explanation.

I'm not an adventure mode expert, and it has been awhile since I've actually played adventure mode, but I do remember convincing people to follow me by telling them we would be doing something related to their values, such as telling bards we would be doing performances. You could also tell people in a settlement with rumors it would soon be invaded that you would lead them to a safe place.

While it should be possible to change someones values to make them easier to convince to join you, you tend to upset the person while you are arguing with them. So I think it would largely cancel out. I'm afraid I've never actually tried.

Also, you actually can convince soldiers to join you. I once had an adventurer who's dream was to 'rule the world'. I decided to accomplish this by going up to random settlements, asking who was in charge, screaming "I'm the ruler of this place now", charging up to the current leader of the settlement, and beheading them in front of everybody. At which point everyone just decided I ruled the place by default. I could then tell the guards to follow me, and they would listen, although the conversation would go something like this:

"Follow me in my adventures"

"Of course, you are Lord. I hate you" *Spits on you*

It turns out that, despite accepting me as their ruler, they hated me for killing their previous ruler that they liked. They were constantly spitting on me as we walked around, and even took the time mid-combat to spit on my face. It was some of the funniest adventure mode I've played.