Hi,
I am not a turner so don't have the large volumes of shaving you produce so quickly, but all of the sawdust and shavings I make in the shop is used to heat it over the winter, along with all the scrap pallets / wood I can acquire. 8) I have a small Yotul wood burner and a long handled shovel, I fitted a bit of large dowel on to a standard one, this allows me to put the dust and shavings on the fire instead of throwing them in through the door.
A word of warning about the second log maker linked to above, I had one like that back in the 70s, total waste of time and effort as the wet logs take forever to dry. You would need to make all of them in the height of summer, have days of continuous sun shine and then somewhere very dry to store them until you want to burn then. The first one on the other hand does look like a usable solution.
There is now a commercial machine that will turn sawdust and shavings into pellets for use in multi fuel burner, I think SL Hardwoods now sell the pellets they make from the waste out of their timber preparation.