The shooting method is a general purpose techniques for solving boundary value problems. As a general rule, a solver specialized to the problem at hand will outperform general purpose techniques -- if such a special purpose solver exists. This is most certainly the case for the two-body orbital boundary value problem, aka Lambert's problem because this problem is central to rendezvous and to orbit determination. A large number of special purpose Lambert's problem solvers have been developed over the last two-plus centuries. You will fare much better if you use one of these domain-specific techniques as opposed to a shooting method solver.
Even then, you'll have to pay attention to delta V. A Lambert's problem solver finds one or more conic sections that intersect the source orbit at time t0 and the target orbit at time t1. Just because a solution satisfies the constraints does not mean it is practical. You'll need to check for transfer orbits that are ridiculously expensive in terms of delta V. This includes retrograde transfer orbits, for example, but also some prograde transfer orbits.
In this day of open literature / open source, it is far better to look for existing Lambert's solvers as opposed to rolling your own. You can find several in the public literature (but sometimes only as pseudocode), and several on github (but sometimes only as student quality code).