Can't help you much with UK breeders but the female temperament isn't universal. My female is so aloof and such a diva that it can be really challenging at times to work with her. On the other hand my male is the cuddly type and crawls into my lap when it's late in the evening. I wouldn't close your eyes to males. You need to find one that fits your personality.
Recently I took my almost 7 year old male to an agility trial (trying to get him used to new places so he can be more calm). As we were waiting in line for our turn, he was actively working the nose, standing on his hind legs trying to find whatever. Didn't think anything of it really although he hasn't exhibited this kind of behavior since he was neutered years ago. Then once we started our run, it took a turn back towards the line-up area. Off he goes to the fencing and again stands on hind legs working the nose and trying to find whatever female must have been coming into heat (females in heat are not allowed in the trial); wasted lots of time trying to redirect him back to me. Is this return to old ways common in older males?
This is how I did crate training with mine ...
Put several treats in the crate and have the dog go in and get them (door open); several times so the crate becomes a "good place"
Then treats and dog in crate with door closed (I'm nearby) for a few seconds; several times and adding more seconds
Then same thing but fewer treats, door closed, I go out of sight around the corner; several times.
Then I go outside the house for 5 minutes, then again for 10 minutes, then again for 15 minutes, etc.
I changed the treats from several tossed in the crate to treat(s) in a kong or other toy to keep him busy.
I kept building up the time with fewer and fewer treats until now they get one biscuit in a kong and I go to work for 9 hours.
The evening part, I simply put the crate next to my bed and did similar thing except in reverse. The crate has a closed door at first but is right next to my bed. Then eventually I start leaving the door closed but not latched. And then I don't even close the door. Now they have a basket they sleep in and not the crate.
My male used to do a 180 as soon as an intact female came in the training center - even if she was on the far side. After neuterization, that went away fairly quickly.
And he did not become agressive or more reactive or any other personality change afterward either.
I see that you did not go the the American Kennel Club breed site:
You will find some different descriptions of these dogs there and I strongly urge you to check this site out. The website will also provide a list of breeders in the Chicago area (there are many there and Wisconsin); most of which will be happy to show you their dogs and talk more about them. I urge you to take advantage of this.
Active - yes - but not necessarily in the way you mean.
If you are thinking of jogging/running with one, good luck. Some people have good experiences but the breed is so highly prey driven that they will constantly be trying to take off after squirrels, rabbits, other critters (biggest killer of basenjis are cars). Your dog must be on a leash if you do go running. If you are thinking of playing ball, good luck. Again some will play but the breed is not retrievers; some won't even play with typical dog toys.
Training will be an absolute necessity. Basic obedience best if learned in a class setting or from the online Fenzi Dog Sports Academy (and please do not buy Cesar Milan training books or videos) - but also impulse control classes, how to self relax, how to meet other dogs.
You will need to spend time indoors with your basenji - mind games (aka tricks, interactive toys, hideNseek games, etc.) will do wonders to create a happy healthy relationship.