But since you aren't happy with the way it puts out new growth and you had a branch (partially die), shouldn't the first priority be to make it as healthy as possible?
I concur, up pot in new mix, or better still take Harunobu‘s advice and put it in the ground. Look for a spot with morning sun- afternoon shade/partial shade, feed it properly, treat it right and it should be bursting with growth by next year. In Fred C. Galle’s book, Azaleas he recommends lots of fine oak or milled pine bark or coarse (rough) Sphagnum peat in the mix. ( I toss in some soil from around one of your other azaleas too, if you have others in the ground, just for fun.)
As far as backbudding is concerned, I’ve literally butchered multiple species of evergreen Azaleas and Rhodys and had them all explode with growth afterwards, with no exceptions as long as I took care of them.
Check this cool care checklist out for once it’s back in a pot. (The months are cattywampus, of course)
http://satsukiazaleabonsai.org/satsuki-azalea-bonsai-care/
When you do repot, I personally recommend a 70% kanuma 30% chopped New Zealand Sphagnum moss mix. After all, you are in New Zealand.
. But use what you think is best.
Once you get this tree healthy, then decide about grafting. The only grafts I’ve seen used on azaleas are approach grafts, not to say others aren’t used. You can see how to do these on Youtube.
Here’s a brief description of approach grafting on a satsuki By Darren Wong in Oakland, CA.
http://satsukiazaleabonsai.org/approach-grafting-by-darren-wong/
Finally, there is an inexpensive book (US $18) called “Japanese Satsuki Azaleas” (2004) that describes approach grafting and lots of other great techniques and shaping ideas on Satsuki. It can be purchased at
Bonsai Tonight.
Approach grafts on Satsuki are mentioned in multiple other books including A Brocade Pillow (1984) and Bonsai Techniques for Satsuki (1979), and have withstood the test of time.
Good luck and cheers
DSD sends