@Quercus:
Please do be seriously overly cautious. Zeus's testosterone is still flowing..it takes a few months to recede. And they are both adults…and Basenjis really don't like having their space invaded, particularly by dogs with no sense of dog decorum (which Boxers lack).
I completely disagree with saying that boxers lack dog decorum. Boxers are a highly intelligent breed, that are very much misunderstood as stupid and such because they more often outsmart thier owners and are problem solvers. A lot of peoples misconceptions of boxers if because there are to many people that don't train their dog and focus the working breed mind.
As a boxer owner I hope I can help some. Boxers will tend to be more vocal when it comes to asserting thier place, and even if it's a basic "hey knock it off an leave me alone". Like you described between Zeus and Giz. I'd give it some time. Boxers over all are a very laid back breed and want to get along with every one.
And of course yes at the moment in a sense you have two intact males in your house, because Zeus still pretty much smells like he's intact, and the hormones are still going through. Because you say that he is very laid back, just have some patients, keep a squirt bottle on hand. And squirt the one that starts acting up. Now granted it might be more Giz, and I'm not saying to punish him for his actions, its more to show him that these actions are not permitted. YES, it is still his house and he was the king, and now there is a big dog, but he needs to learn that "nasty" behavior should not be accepted at anytime. And same for the Zeus, he needs to learn that the smae behavior is not permitted either and that slobbering the Basenji is not a correcting thing to do.
Boxers like basenjis are vocal dogs, but because they have a deep voice it can sound quite awful, my boxer Reggie sounds like a lion when he does it. He's 5 now and I've seen him like you described only a few times, and not to sound like I'm defending Zeus because I didn't see the whole, thing, Reggie only will get that way if the other dog starts it. We have a friend that has a cocker spaniel mix that snarels and nips at Reggie all the time because she's very jealous over attention and is very possesive over her chewys. Reggie has only put her in her place once, and that was after she actually drew blood on him.
Please feel free to ask all the questions you need, especially about boxers, we used to have a neighbor that had a basenji so I know that they can get along.