Howard et al,
Contrary to the popular belief, many moulding planes can be used for cross-grain work. The cutting geometry of bead planes is not ideal, so they can present some difficulties, but I've had good results with a variety of other moulding planes for this application, including ovolos and H&R's. The irons need to be accurately profiled and very sharp, and the depth of cut adjusted for the material being worked. Needless to say, it would be a good idea to experiment on some scrap wood of the same specie first.
Blowout at the end of the stroke is an issue, so that needs to be dealt with. One of the advantages of working with H&R's in this situation, is that they can be used from both ends of the cut to help address this issue. Also, as you probably know, it is generally best to do the cross-grain work first, then finish up with the long-grain work.
The cross-grain surfaces will have a more matte appearance, but the disparity can be minimized with some very light sanding of both types of surfaces if it concerns you.
Don McConnell
Eureka Springs, AR