Two instead of one won't stop the digging. My girls were busy with a hole to China back in the day, but I didn't care because it was in a dedicated dog run and not near the fence where they could dig under. Digging is a hard habit to break. As far as the house is concerned, a seven month old pup likely shouldn't have the run of the place when you are out. I don't like crating, but have always managed by restricting the dog to one or two "safe" rooms when I can't supervise. All of mine have graduated to being more or less reliable in the house, although I have made some rooms off limits. My current boy is not destructive at all, and I don't restrict his access. I like your solution of giving him the backyard with house access only to his crate. This seem pretty ideal to me, although it does nothing for the digging issue.
I do believe in crates and I don't believe in dogs outside when I am not home, so I am not much help, sorry. Had a dog bit by a snake, regular news of dogs poisoned or stolen from fences… I just prefer my guys inside and safe. I never had to crate other breeds after puppyhood, but crating basenjis for life is not at all uncommon when owner isn't home due to their destructiveness.
Not sure of your finances and ability, but a kennel run with pea gravel should stop the digging and destruction. Throw in GOOD toys that are safe to play with, make sure the top is covered to protect from sun, and you can protect the yard and house. My friend's kennel below is great, but the same thing on the ground with gravel would also work.
Don't know who your pup's breeder is, but I have never seen a Basenji "mellow" until 5 or 6yrs!!! and the minute you think they are perfect little angels… they take that opportunity to prove and show you they are NOT! As far as the house, I would never leave mine unattended loose at that age... maybe at 2 or 3... and for a very short time?
I have never had a digger, so can't help you with that... but off hand, sounds to me like he really is not getting enough excerise, especially mental excerise. Do you take him to any training classes? Do you do any training at home to engage his brain power?
Who is his breeder? Many of us are related by our Basenjis
I came home today for lunch to Dolce chewing the plastic bottom part of her metal crate and ripping up the carpet. I don't really even have a carpet in the area anymore lol. So frustrating I definitively feel your pain. She pushed her toys out of the crate and I guess was trying to get them back chewing her way out hahah.
Thank you all for your replies and suggestions. Its just really frustrating that I'm always wondering what kind of destruction I'm going to come home to. I do enjoy his company when we're together. Buddy is so smart, easy to train and very affectionate. The little s#*t just waits when I'm gone to bring out his horns 
He just got neutered last Friday and he's recuperating just fine. He just seems more stuck to me lately since he came home from the vet (probably start new thread on this).
I cannot leave my dogs out and they are older, even the 11 year old will chew! I have all kinds of chew toys out and they will sometimes chew on them. One of them had dragged the crate pad outside that I use for them to lay on inside the house and some of the stuffing was pulled out of it. This is one of the things I do not like about Bs-the chewing even when they are older. I even crate them when I take a shower but I cannot trust them. If one does something naughty then usually the others will get involved. The only B I have ever had that did not chew was the 15 year old BRAT rescue that I was fostering. My dogs are good in their crates though so I guess I should not complain too much!
I have never had a digger either (thankgoodness!) unless they were digging for a bug or smelled something in the dirt. I think Bs are relinquished to rescue at 2 to 3 years old because they still act like puppies and the owners do not understand that. I guess once the dog gets fed adult food owners think they should act like adults-no chewing, etc. and that is usually not the case for Bs.
Doggy day care helped Arnie and my younger rescues when I lived in Houston as they could get exercise and plenty of socialization.
Jennifer
I feel a little scared about dog day care and of other people taking care of my dog.. what if they have people who do not know what they are doing really and my girl gets out or something happens.. I worry so much!! I know she would have fun but I'm not sure what its all about really.
hmmmm, Blaze didn't mellow out until he was about 13-14 (and he could still outrun a 9 year old border collie and a 7 year old lab). Then I could leave him loose in the house alone. A Basenji with no teeth and partially blind is not all that destructive… I believe in crating, and Cricket loves her crate. I also got her a boredom buster food ball so she's kept fed, and amused.
hmmmm, Blaze didn't mellow out until he was about 13-14 (and he could still outrun a 9 year old border collie and a 7 year old lab). Then I could leave him loose in the house alone. A Basenji with no teeth and partially blind is not all that destructive… I believe in crating, and Cricket loves her crate. I also got her a boredom buster food ball so she's kept fed, and amused.
That's very funny. Trust me, I have the buster cube, busy buddy, kongs, treats, ropes, bully sticks, nyla bones…I just don't think it's enough to keep my pup occupied while I'm gone.
The bottom line on this is that dogs are pack animals and don't like to be alone. Unless they are tired or confined, puppies will amuse themselves in ways we are unlikely to approve of. Usually as they get older they outgrow this tendency and also get to know what actions will earn them disapproval. Unfortunately many Basenjis don't give a rat's patootie whether you approve or disapprove of their actions, which is likely why as adults they still seem inclined to cause you grief.
In my experience, if they don't have a lot of opportunity to "practice" the "bad" behaviour while they are young, they seem less likely to continue when they are older. In practice this would mean crating or otherwise confining them to an area where they can't get into trouble when you are unable to supervise. I also believe it is much easier to end up with a trustworthy older Basenji if you were home to supervise much of the time when they were young. Having the opportunity to correct unwanted behaviour is superior to just preventing it by confinement, as the dog actually has an opportunity to learn something. In these days of absentee owners, perhaps the best solution is something like doggie daycare if it is available to you.
"I've already talked to the breeder and she said that they typically mellow out after a year " Your breeder is nuts. I have a 3 1/2 yr old female who still needs to be carefully watched and I need to protect my "stuff" from her which is sometimes difficult, when she is in a high energy state and hasn't had enough exercise. Remember - a tired dog is a good dog. I DO agree that getting him a companion will probably take care of most of it. His destructiveness when you leave may have something to do with separation anxiety, or just plain boredom. When I leave now, both my girls go to sleep or at least do not ruin anything, and neither of them is crated. It was almost instantaneous when I got the companion dog, who is a basenji mix.
Or getting a "companion" could mean DOUBLE THE TROUBLE!!!
That is so true Pat! They could teach each other bad habits.
Jennifer
I've always had less issues when I have one rather than two, but OTOH, if I was out a lot I would want the second one as a companion. I don't think it is fair to leave them alone for hours every day.
(Basenjis are smart enough to figure out that when they do something all they have to do is act cute and let you think it was the other one that did the deed!)
