First, do something about the rabbits. No point promoting more low shoots if the rabbits are still about.
Deciduous azaleas are not my usual but they still bud on bare wood so if you want growth lower down just chop the long stems. It's not technical. Azaleas will sprout anywhere along the stems if they are pruned. If not pruned they just grow from the tops of the stems.
Usual time to prune azalea is soon after flowering because that's when they normally start to grow.
There's no way I know to get new shoots on a long bare stem and still keep the stem long. It will always try to grow from the tips if left alone.