Matt - you need to realize that you are using a non-syncrmesh gear box and learn how to shift it properly. DrEntropy's "stutter-shift works well for shifting up, but you will need to double clutch when shifting down. It takes some experimentation to find the correct speed vs rpm where the gears will slide into mesh without grinding, but once you get it down, you will find that you don't need to bother with the clutch other than when starting from a complete stop. It all works a lot better if you shift at a relatively low rpm (one can't hot rod this car with a non-syncromsh box in it). Once you get the process down pat, you will find it is a lot of fun to drive - I drove a 1936 PB from Washington state to Southern California many years ago and never had any problem with the gear box or with shifting it.
Cheers,