Hi and welcome to JOF.
I have a similar setup on the tongue to what you are describing. I have the Arvika (original developer of the concept, and I understand it to be much stronger and better built than the SC version) receiver on my X19H. We use a Thule CrossTrak which does have a lot of extension on it but it clears the back of my Traverse. A couple of pictures:
Yes, it will probably be fairly close to your cap, but mine does clear the back of our SUV. with only about an inch to spare on hard turns. There are racks out there with shorter extensions however.
Note that the JackIt listed above probably won't work for you if you want to be able to move the rack over to the truck as well. I also don't like that it puts the point load almost directly over the tongue increasing weight there. The Arvika/SC option is a couple of feet back from the tongue, so TW effect will not be as large.
ETA: another consideration is that the rack MUST be removed to drop the bunk, although the Arvika components sit just low enough that they do not obstruct the bed.
EATA: ignore that last point. Just realized you wrote 17BH. Was thinking X17. Not a problem you will have!