Nice project.
I have some apple wood drying for a bowl project....not sure when that will ever happen though.
When I carve green wood, I generally get my project (spoon) roughed out then either put it with a large amount of shavings into a plastic bag in the refer for a few days....to stabilize the water content.
Then I remove it from the refer and bury it in shavings in a big rubber tub....moveing it "up" in the shavings each day until it is on the top of them. By the time I have worked it to the top of the tub it is fully dry and ready for final work.
Some people put their rough bowls etc in a paper bag to slow the drying but I have never found that to work as well as the shavings and refer approach.
This long birch bowl is about 1/2" thick, I carved it fully-green, and I spent probably 2 weeks moving it around in chips to prevent it from splitting on me.