I think I know what you mean about a "time suck."

As far as alternative logics, we can skip the one that says all contradictions are true. But Dialetheism says some contradictions are true, and focuses on examples like a person leaving a room. At some point he is both in and not in the room. These area easily addressed since LNC says "at the same time and in the same respect." In one respect he is in the room, in another he is not in the room.

But if one were to press the point and say "no! it is the same respect" then I'd take the discussion to the level of meaning. What does it mean to be both in the room at the same time and in the same respect? I'd argue (although if you want it fleshed out I don't have the time now) that this is meaningless.

So I don't think that presents a real problem.

The infinite regress for internalism is stopped by noting that there is a basic level that cannot be questioned (how do I know?) because it makes questioning possible.