The best way to start a collaboration is to engage in a face-to-face brainstorming/working session so that you 1) formulate a problem of a mutual interest, 2) jointly sketch a scaffolding of a joint paper, and 3) come up with a plan to proceed, or at least agree on how to arrive to such a plan. Before the meeting consider the topic semi-open (unless you are dead-sure you know what you want to work on with the person), you never know what new/interesting/unexpected will come out of your discussions.
Now to get to a meeting/a few days stay, you need to arrange for a visit at the (future) collaborator's place and it seems that what you are asking is about a particular way to do that. From my personal experience, there is no right, nor a wrong way to do it. I understand these things in terms of signalling. That is, the form is less important that the signal you are sending. In my opinion/experience it does not matter whether you write a short notice like
Hello Joe, we met there and there and I got intrigued by the topic we discussed. Would it be possible for me to visit your lab/group and expand on those ideas? Fred.
or expand in a two-page argument about why it is beneficial for both of you to meet. In both cases the signal is the same: would you be willing to speak to me? and that is the only thing which matters.
And you should read the reply in exactly the same manner. Whatever is written there, the only thing which matters is whether the answer is yes, let's see what comes out, or no, blah, blah. All the rest can be discussed during the meeting, given the reply is positive. If it's negative, most probably the collaboration wouldn't work out anyway. Being open-minded is a state of mind, a personality trait.
Now to your concern about the collaborator's higher rank/position at a prominent university: I do not know about the culture and social interactions in communities concerned with humanities, but my general observation is that the better a scientist (whatever better means), the more humble and modest the person is with respect to the corporate structure and seniority ladder. That is, the majority of really good/respectable researchers in my experience do not care for your rank, they care for what you say.
The point I wanted to convey above is the following:
if the person you want to collaborate with is open minded and thus a potentially a good collaborator, it does not really matter how you approach him/her, just do it. In the case you have something important/significant/novel to say, he/she will engage you and the collaboration will start. Just remember, it's you who approached the other party, hence you want something from her/him, therefore it is important that you understand that you will be the driver of the collaboration, at least at the beginning - the ball is initially on your side - unless you touch a topic the other party is working on and has some solutions for anyway.