Dave - my only experience pruning that way
has been with ramblers - my husband will often
take a gas powered hedge trimmer to a well
established growth of 4 Red Cascade.

However, I also have rabbits who have a
tendency to do straight cuts on some of my
roses. Most do just fine and grow back without
a problem.

Given your specific problem rose, what about
an experiment? Prune a cane or two with
the straight across method, at the same time
prune another cane or two using the traditional
method. Keep track of how they do.

Good luck!

Gail