Is an engineering PhD enough to publish math stats research? I'm in the second half of an electrical engineering doctorate but have come to realize that mathematical statistics and the theoretical side of information theory might be more my calling. I am too far along in my research to pivot my doctoral thesis to this abstract of an area, especially considering I am in the engineering department.

I am relatively strong in math (Tall for a hobbit... taking the grad functional analysis sequence, albeit late relative to when math students see it) and have a (very conservative) original math side project, so I believe I am at least capable of understanding math research. However my environment is still most conducive to studying engineering problems, not math/stats ones. 

If someone in this position wanted to research and publish in mathematical statistics later on, would an engineering doctorate be enough credentials to do so?

There are several reasons I ask: 


The amount of math knowledge implied by a typical engineering doctorate is not anywhere near the amount necessary to do research in statistics theory.  (Not to say the EEs I have met here aren't extremely capable in their field,  just most aren't focused on research level math). 
The direction my adviser and I are headed with my current thesis is interesting and useful. I'm not about to drop my engineering degree.
If it isn't necessary I would rather not jump through all the hoops of getting a PhD all over again.
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.