We are thinking Spike might be a Basenji Terrier mix. He definitely has the basenji personality and the bark. We love him no matter what he is but we are curious.
Now I look again Portuguese Podengo could well be in there to a large extent. Lovely feisty little dogs. One smooth one I know quite well is very similar in size to a Basenji but shorter in the leg
We also have a possible Basenji/Terrier (Yorkie) mix. I've had some doubts, but seeing this picture of Rosie, I can't help but see my Rebel. Such a great looking dog, and if she's anything like our girl, you're in for a treat!
The traits you described are also found in most of the Nordic/spitz type dogs. I don't see anything overly basenji-ish about him in the pics. What ever he is, he's very hansome.