... this chihuahua ... and my basenji will chase one another for an hour at a time and constantly bite and push at one another. My basenji loves to grab the chihuahua’s scruff and pin her down, but she’s never actually attacked the pup.
This is just playtime -- my "doodle" and the other dogs (her size) do this at the dog park and just have a blast. They aren't actually biting. There is no blood, and each one gives as much as gets. It's like they are playing a game of "tag". There are times when I put a stop to it, calling doodle's name and then a command, either "stop" (if everyone is getting too rough) or "gentle" (if she's playing with a smaller, or more submissive dog). She is really good about it.
I think your basenji may be trying to get your cat(s) to play the same game, but we all know cats don't play like that. Almost sweet that she starts grooming them when she catches them. Almost. I would probably be apprehensive, but you've watched them for three years -- so my concerns may not be warranted at all.
My chihuahua always growls (not in a mean way), even if the basenji is just simply walking past her. It leads me to believe that my basenji is taking on growling as a form of communication for when she’s attempting to play with the cat (as my chihuahua does with her).
I agree, your basenji has learned this behavioir. But if you want to succeed in teaching the Basenji not to growl, you also need to teach the Chihuahua not to growl. Fair is fair and it's not fair to fuss at one dog for doing it and let the other dog get away with it. You don't need a leash. Just your voice. When you see or hear the undesirable behavior you call their name then give them a command. If it's the growling, perhaps "name, hush!", and then "good dog" for listening. You need to use a firm voice, not a whisper, not screeming, but a firm, no nonsense, "hey! stop!".
Does anyone know of any instances of their basenji(s) growling when playing?
Yes, doodle was playing with a big boxer mix (last night) and the boxer was growling during their game of tag. doodle was zipping in and out around the park obstacles and this boxer was never going to catch her, so he would growl if he got close. doodle wasn't growling, the boxer was, but same concept. The boxer wasn't being agressive or warning of and attack, they were just having fun. When they stopped running to catch their breath -- zero animosity between these two.
Which is much like what I'm thinking is happening at your home, when the game ends, they all get along... because it's just a game.
I agree with elbrant....If you want growling behavior to cease, you must correct it in BOTH dogs. Basenji are very good at learning from their humans AND from other dogs. I had a purebred Basenji that taught herself to make a reasonable imitation of a bark-she learned from the other dogs at the dog park!!!! I would make a really concerted effort with the chihua-once she starts to curtail HER growling, I have a feeling you will see less from your Basenji, too.
Listen to your gut feeling. Stop any behaviour that you're not happy with, eeefarm makes a good suggestion to enforce the stop command by having a lead attached that you can step on when necessary. Your B may just be copying by growling but remember she may not! Yes, Basenjis will growl as they play but the meaning is usually fairly obvious when you watch or listen carefully. It appears that you have quite a complicated series of events - try to deal with one thing at a time but always be on the alert. As others have advised, please don't leave them alone together when you're not there. As you indicate that she has a hard head with the rest of the family this would still apply when you're away. Eventually, with determination you'll obtain equilibrium.
One thing that may have occurred but perhaps gone unnoticed is that the cat or cats, feeling insecure in new surroundings, may have reacted and taken actions, either aggressive or submissive, that changed the dynamic with the Basenji. In any case, caution is always advised even with animals that have coexisted peacefully for some time. If a cat shows disrespect to a dog, it can trigger an unfortunate reaction. My friend's Jack Russell killed a cat it had previously been friendly with, possibly because the cat took a swipe at the dog. Basenjis are not typically as volatile as Russells, but many do not tolerate what they perceive as disrespect.
Moving house upsets most animals
While I agree with this, I'm confused... I didn't see anything in the OP that indicated the household had moved. (?)
How about this? " I just moved recently and she’s back into the entire chase and pin motion with the cats."