pbass I have gassed on at length of my love for fixed on gravel but in your case I agree with most of the above that freehub with brakes would probably be more fun.
Fixed gear is all about the drive train and on trails while attached via straps you really want to be confident in what you're cranking if
that's all you be doing (i.e. not coasting ever).
OTOH, if you part up nice SS stuff on the Cross Check then it'll be that much cheaper to build a dedicated-fixed bike and then return the Cross to its other format if so desired