I guess there are several things to consider.
Are you turning end grain? If so use a log large enough that you can cut it so you aren’t having the pith in your box. Or consider turning side grain also with the pith cut out.
Other things you could do is turn the pice oversized and dry it in a paper bag with some of the shavings for a few weeks and then returne to the final size.
Just a few thoughts hopefully someone else will have some thoughts also.
Good turning
Russ Bolton