Good Afternoon, Ara,
The 23C should have no trouble covering 6 x 7, since it's designed for up to 6 x 9. Either the condenser positioning is wrong, or the lens won't cover properly. If the enlarger is adjusted for 6 x 9, the problem is almost certainly with the lens. For years, I used an 80mm Schneider Componon for 6 x 7 with no problem as long as the negative was properly centered. My newer 75mm El-Nikkor won't handle 6 x 7, so I now use a 90mm for that size. As to a 4 x 5 enlarger, one would be highly desirable for various reasons, but it's certainly not necessary for a 6 x 7 negative.