"In order to get along with a Basenji, you have to be at least half as smart as the dog!"
Welcome to the forum. You might have more luck looking for a dog sitter or house sitter. Of course, with Covid 19 precautions someone might not want to be coming into your house or you might not want them there. Right now not too many people are travelling, but there should still be boarding facilities somewhere near you. Whether they are suitable for a Basenji is another story. I had dog walkers to take care of my boy when I was away. They would come and walk him three times a day and spend the night at my house. (and sleep with my dog!)
Oh, sure. How long before someone gets bit in the boob by an enthusiastic dog? Right up there with spitting treats at your dog to get him to look at you. (some "trainers" actually advocate this!!! But only the ones who don't understand how to train such a simple behaviour). I think if I needed to keep treats handy I could find a better location, although granted some clothing doesn't have pockets.
I never wasted my time with "no" when my guy got hold of something off limits. My scornful "Is that yours?" usually had the desired effect unless it was something particularly attractive to him. And I certainly have pried my share of forbidden items out of mouths! It irks me when I see dog owners ignoring a dog who is busy sniffing and then ingesting God knows what! If you are unlucky it can cost you a vet bill or worse. (but then, I am a control freak. Difficult with a Basenji!)
@DonC, you are right that attention is key, but in this case paying attention to the dog at all times when walking is absolutely key. Letting him get used to scavenging on walks will be self rewarding, and something that should be avoided. Best not to use a flex lead so he is close at hand and can be observed. Apart from anything else, it is dangerous for a dog to pick up things on the road. Poison or splintered chicken bones can be the result. The person on the end of the leash needs to be guarding against this.
@eeeefarm She was just in one home. She was in a few shows, but was too shy, which is why her breeder was seeking to rehome. It's encouraging to know that someone else's b went from biting to loving!
Thanks for filling in the blanks. This girl is likely very confused, missing her breeder, and the familiarity of being in a setting she is used to. It's likely she's had multiple dogs around, and all of a sudden she has lost her friends, her humans, and finds herself with strangers. Of course she will be confused and upset about the situation! Give her time, don't force things, let her come to you, and be as "matter of fact" as you can. Fussing over her will not be helpful, let her approach you on her terms except for when you must take the initiative. And make sure others in your household respect her space. With a little time, this situation will resolve, but you can cause a problem if you push to have her accept you.
Give it a little time. At 3 1/2 years old, moving to a new home is likely to be a difficult experience and it will take time for her to trust you, and to understand that this is a permanent change in her life. My boy Perry, who I adopted at 3 years old, bit me the day he arrived! And I had a couple of other incidents with him early on. I got the definite impression that he felt he was "just visiting", and it was the better part of a year before he seemed to be truly at home. Not that he went around biting people, but I was careful after that first incident that I did nothing that could feel threatening to him. He turned out to be a wonderful dog.
What is your dog's history? Has she been bounced around a lot, or just in one home up till now? If the latter, she may be quite confused at this turn of events.
You might try training "It's your choice". Since you are already into clicker training you are one step ahead. The point of the exercise is that the dog only gets the food reward from your hand, never from the ground or the floor. Once you generalize the behaviour it should help to control his scavenging, although you will likely have to "proof" him by setting him up quite a few times. And you need to be quick so he doesn't self reward. However, it is a good thing for a dog to learn, and if properly trained will prevent them from grabbing food inadvertently dropped on the floor, or helping themselves to an unguarded treat. I hasten to add, it isn't the easiest thing to train a Basenji, and you have to be absolutely consistent! A basic training video here..
I'm with tanza on this, better to avoid the dog parks, but if you must then use the large dog side if there is a choice. And although I have used an e-collar for safety when I took Perry for off leash walks on the farm or in the forest, I would be wary of using one at an off leash park. Too much chance of confusing your dog if a fight broke out. In Perry's case I would never have considered exposing him to other dogs, as he was quite dog aggressive.