Thought I'd give a follow-up. I went ahead and installed the zerk fitting and pumped in some Valvoline Cerulean grease. Seems to work fine and has fixed the problem to a certain extent. I don't think any lubricant can totally fix a binding condition, which I'm fairly certain this is, but the steering feel on my Z4 has improved considerably with the grease in there.
Why the Cerulean? I learned that lithium complex greases are the most widely compatible so I went conservative. Cerulean isn't synthetic and doesn't have a lot of exotic additives so it's pretty basic mineral oil grease. Seems to help a lot with my problem.
Truth will always bear up against falsehood, as oil does above water