You've done a god job of planning.
The UHaul-installed Curt hitch receiver looks like a good choice.
The Anderson WDH looks like a good choice.
I am not familiar with the Redarc brake controller, but the description sounds good. As long as the description contains the word "inertial" or "proportional", it is good. If it contains the word "time" or "delay", it is a bad choice. If you want to consider a different unit, a very common and excellent choice, especially for new users, is one of the Tekonsha series. It has the advantage of being very widely used, so help and operating expertise are readily available.
When you said "prewired" in your initial post, I assumed you meant that your vehicle already has a 7-pin connector (often called a Bargman connector) mounted near the hitch receiver. It would look like the attached picture. When you raise the little door, you see 6 flat blades arranged in a circle, and a pin in the center of the circle, for a total of 7 contacts. Your TM will come with a cord that mates with this connector, so you must have one of these. If you don't have one, I'm not sure what you mean by a "round 7-point wire harness", so I may have mis-advised you. Can you clarify?
The wiring for this connector looks like this
https://www.trailmanorowners.com/for...&pictureid=442
Bill