So, here's our first night update. I got into bed while my fianc? was walking Loki for the last time before bed. The hope was that maybe if I was already in bed, he wouldn't freak as much. Fiance walked Loki upstairs on his leash. However, once he let go, Loki jumped up on the bed and immediately went into digging and biting the sheets, so it doesn't appear that me being in bed first helped. However, we immediately pulled him off of the bed with the leash on and made him sit (no treats, but praise) and calm down. This probably went on for about 10 or 15 minutes - he'd jump up, dig, and then get pulled off and corrected.
After the last couple times of leash corrections, Loki decided that it was time to assert more, and started his sprinting and biting us. I immediately grabbed him, "bear hugged" him, and stopped him with a corrective "NO biting." We went through this probably three or four times, as when I'd let him go after he calmed down (and received praise), he'd go right back to biting and sprinting, but the last time, he stayed seated on the floor while I got back into bed and fianc? brushed his teeth. He waited to come back up on the bed until fianc? called him, and when he jumped up, immediately put a toy in his mouth, laid down, and went to sleep.
So all in all, not an awful start. I must be honest that I was relieved to hear you say that you use a "bear hug" on your dogs. I have done this before with other dogs I've owned, but was told that "you can't do that with a Basenji." However, I think different techniques work better for different dogs, even of the same breed. We will see how tonight goes.
Thanks again for everyone's suggestions!