Is an engineering PhD enough to publish math stats research?
No formal credential is required for scientific publication in any discipline.

What is required is good work, presented well in a context in which the reviewers can understand your results and their significance to the community with which you are communicating.

That often strongly correlates with having a Ph.D. in the discipline in which you are publishing, since that is the most straight-forward manner in which to acquire the skills and knowledge necessary for effectively engaging with such a community.  There are many other ways to get engaged with a scientific discipline, however.

For example, you're coming up on another good opportunity for shifting between communities, however, which is getting a postdoc in the area in which you work.  Given what you have described of your situation, I would suggest following through to completion with your Ph.D. work, while simultaneously continuing to explore your alternate interests and looking for a good postdoc to help you shift.