We have had the same two problems–the harness chafing at the shoulders and pulling. We went through 4 harnesses in the first 3 months we had Ella, but the one that finally worked for us is the Premiere Easy Walk, size s/m. They make a small and medium but they also make a tweener size of s/m that seems to be the best Basenji fit. Because our girl is such an escape artist we also have her hooked to a martingale collar too. The leash clips into both rings together and she is totally secure.
The nice things about the Easy Walk is that it does not go over their shoulders so chafing is not a problem. It kind of goes around the side of the shoulder. But because it does not go over the shoulders we did not feel 100% secure that she could not get out of it, hence the addition of the collar. She wears a collar with her tag on it all the time and we just put the harness on for walks. Also, the Easy Walk is really easy to put on the dog. The Easy Walk has the clip in the front instead of on top of their shoulders. When they pull it sort of pulls them a little sideways, which seems to be a decent deterrent. This does make it a little awkward and you have to guard against the leash getting caught up in their legs. You get used to it quickly. I will also emphasize that we were (and still are) working on leash training and that is thing that has had the most effect as far as pulling. I don't think any harness or collar will stop pulling without training but a good harness certainly can help.
FYI-Our training was basically rewarding (with treats) walking correctly on the leash, even if it was only for a few seconds at a time on a 30 minute walk. On some walks she didn't earn any treats. But after about 3 walks a day for about 3 months, she really started to turn the corner. She will never be perfect (and she has her moody days) but she has already gotten good enough that the walks are pleasant. On a day last week when she was backsliding and being bad on the leash it reminded me how quickly a pulling Basenji can be so frustrating. As with everything related to Basenjis, the keys are time and love.