What can I do to speed up process of us marshells moving my husband to federal prison out of county jail after being sentenced?

YOU have zero input on the legal process after judgement.

You can do nothing, and in fact there is little that can be done, he is waiting most likely for a opening in housing, at the intake facility or at the prison that matches his security level.

There is no requirement that he has to be moved, as long as his rights are given