Basenjis will eat grass if there is something in their stomach they need to dislodge, an itch which needs scratching -
Definitely a trip to the vet because there could very easily be something lodged somewhere even if it is not large enough to cause a total blockage or affect the stool.
I don't like those denta sticks - won't give them to my pack. It does sound as though you are piling in the food even if he is only getting one official meal a day - and that quite late in the day, so not that much time for running around or digesting it all before sleeping.
Why not feed him in the mornings and cut out the noon-time snacks ? You might find his digestive system copes better.
Mine get two identical meals - at 8 am and about 6 pm. Feeding twice a day makes it much easier to control their weight and obviates any need for snacks.