a middle ground, which didn't have a separate tag and did not truly fit neither of the present tags.

Perhaps "Please hug me," "Please ask first," and "Please don't hug"? Not quite a solution, for reasons to be discussed shortly.

I don't know if having a new middle-ground tag would fix this problem.

The underlying problem, I suspect, is the different desires for physical / social intimacy. So long as that exists, you're going to have some level of awkwardness and deadweight loss, and the question is where it falls. Similarly, the underlying reason behind a 'please ask first' tag is that there are people you want to hug, and people you don't want to hug, and oftentimes the people you don't want to hug want to hug you. So even with a 'please ask' tag, they ask, and then you say no, and then there's awkwardness, especially if you just hugged someone else, say, or want to hug someone else immediately afterwards. Perhaps it is enough to acknowledge the costs- having to check tags, having to ask, having to deal with rejection- as the price for when things do work out.

(One of my friends was in a theater group that would have cast parties after the show where, basically, everyone was assumed to consent to make out with anyone else- and she described the experience as "trying to catch the people you were interested in while trying to avoid the people you weren't interested in," which led to a large amount of circling around the room for a party.)