Does anyone know if .22 sensitive targets will initiate the larger, "high power sensitive" targets? I know some shooters who don't have any centerfire rifles but they love to shoot exploding targets. I figure if a rimfire size target can be stuck to a normal exploding target, that would be a win win for them. I mix my own anyways, but I would pick up a package of the other ones if necessary.

I think that it depends on the make up of each binary.  However, I've read of at least one person trying and the rimfire target did not detonate the rifle target.  YMMV.

It works tape them together. If it is that flash based finer powdered rimfire targets.
That is the only kind I have tried it with I can get the brand name some other time if you want it
But it always works for me.

Sureshot?