As Jules says, i think, possibly, finer sawdust (if you can get it) would be your answer.
If theyre leaking in storage, surely youre burner is becoming 'klinker'd' up?
But, if youre otherwise happy, i too would suggest some sort of lidded bunker. At the end of the season, you could chuck in sawdust, and dig out the base, reddy for reloading?
As a side note -
How are you measuring the fire temperature? (just wondering if you have a way i have not thought of?)