I think your plant is salvable if you wanted to work at it, but it would take 3 years to do it right.
The best way to treat shrubby plants like burning bush is through renewal pruning, usually done in a 3-year repeating cycle and consisting of cutting away one-third of plant material each year. In the first year cut the heaviest 1/3 of the stems back to ground level in March/April. Next year, remove half of the remaining old wood (1/3 of beginning plant mass) back to ground level. During the third year, remove all remaining old wood back to ground level. During the course of the three year span, thin any new shoots to the preferred size and shape. At the end of three years, the shrub consists of all vigorous juvenile wood and you can start the cycle again. That type of pruning will allow to keep multi-stemmed/trunked plants looking good indefinitely. The error was in shearing the plant back instead of actually pruning it, but now you'll be ready for next time.
Al
