I have been cutting pen blanks across the grain for ever it seems however in spalted material the most exciting can be had with the grain what appears on the surface can dissapear as you turn, the exception IMHO is Olive Wood that most always livens up cut across the grain.
One of our precious to me is Hairy Oak that cross cut can resemble a Tigers skin the way the striking medullary rays go when cut at right angles. Be prepared for another degree of difficulty cutting end grain is totally different to with the grain, no heavy cuts.
Kind regards Peter.