I'd also suggest you check the string height at the nut. By your description, my first guess would be that the nut slots are too high. It's easy to check. Here's how.
Press the lowest pitched string as if you were going to play the third fret. But…
I began playing clawhammer banjo 3.5 years ago. I have a very bad case of BAS (Banjo Acquisition Syndrome) and own some wonderful instruments including two Chuck Lee custom models. This week I purchased a Gold Tone Cello Banjo and I love the low tones that it produces.
I love to sing the songs of the 10's, 20's and 30's and am addicted to the 6 Janet Klein albums I own.