Threading the dowel through pill-shaped holes in the felt caused too much distortion of the fabric. Cutting slots across the direction of the dowel allows the fabric to conform with less distortion.
Due to the thickness of the felt, this method still caused a lot of distortion, so I tried cutting longer slots
For this thickness and pliability of felt, and using a 6 mm dowel rod, an 18 mm slot gives a good tradeoff between security of the fit and distortion of the material.