One problem I have with the interaction pillar is it tends to be one PC talking to a DM. Does anyone have any advice for minimizing the DM-PC talk time and maximizing the PC-PC talk time?
Be more pro-active in your encounter design and GMing of it.
If most of your combats were formal duels or jousts, you'd have the same problem. But I'm guessing that they're not. Rather, you have ways of putting pressure on the mage (and his/her player) as much as the fighter (and his/her player) to get involved. There are two main ways: multiple opponents confronting the PCs, some of whom attack the mage; or an opponent that the mage doesn't want to let the fighter deal with on his/her own (eg because it is too tough for the fighter).
You can do the same for social encounters. If you have multiple NPCs/monsters, who are interested in talking to (and perhaps want different things from) the PCs, you can generate a relatively dynamic social encounter.
Here is a link to one example of the sort of thing I have in mind.
Even if you only have one NPC/monster, you can still get multiple players involved in the same way you do in a combat: make the other players have an interest in bringing their PCs into the situation. One way of doing that is by having the NPC/monster interested in things that the main negotiator can't resolve on his/her own (eg because s/he lacks the authority - say if a bribe is wanted out of party funds, the whole party have to get involved to make a decision and negotiate the terms; or because s/he lacks the knowledge - say if the NPC/monster is wanting to talk about some point of historical or religious detail, another PC or PCs may be the ones who have the relevant information; etc).
Here is a link to one example of the sort of thing I have in mind.
Another way of doing this is by having the NPC/monster push things in a direction that not all the PCs agree upon. So then the PCs (and hence the players) have to resolve a disagreement or difference of opinion among themselves.
Here is a link to one example of the sort of thing I have in mind.