Hi Tom,
I'm thinking Velcro on the back of your new mounting bracket, and on the
dash.
If there's not enough flat surfaces to hold firmly, you might be able to
fasten a flat piece of something to the back of the mike bracket first.
Another approach might be to put a wire or cord through the holes in the
mike bracket, ending with a loop at the top to hang over your existing hook.
73 Jerry Handel KA3ROC