Regrafting a rose?
 

I have a question and a problem ...
My rose garden has gotten as big as I can support .. about 60 roses ... and
I would like to make some changes.
All the roses have been in the ground for several years now (some for many
years). I don't like the blooms of several newer ones. I COULD just dig the
rejects up and discard them, but I would like to try cutting off their canes
and graft on canes of some other roses. I've had success with grafting a bud
of another rose onto a young, strong cane, but when the cane died, the graft
died.

Has anyone had experience doing this? All roses in question have large,
barky grafts. I was thinking of trying cleft-grafting, but it seems like all
the new bulbous graft growth is the new variety. Would I have to saw off all
the growth on a graft down to the original stem to get rid of the previous
rose? Would it be better to try bud grafting, or cleft grafting onto the
original stem?

It just seems like a waste to pull out a rose with strong, healthy roots if
I can saw off the existing canes and somehow regraft it.....or would cutting
off the top-growth canes just cause the rose to sprout suckers from the
roots?

Thought I'd ask before trying ... Thanks to a great group!
Sue in SoCal - zone 10