Getting rid of first degree to apply for second
Don't throw out something you already have. If your goal is to do research and write some papers, then you can in essence do that in your spare time. If you're good, people will want to collaborate with you and mentor you whether you're a graduate student or not. In other words, I don't see the reason why you want to go through graduate school a second time -- having to take all of the classes again, take qualifying exams again, etc. All of that  doesn't help you in your goal, for which you are already qualified because of your previous PhD.

Of course, it may be that you want to go back to be a grad student because it usually also includes a stipend, health insurance, etc. But you can get that from other sources as well: You could do research in your spare time, or simply have a part-time job so you have more time for research. A good part-time job may in fact pay no less than a grad student salary.

A particularly useful choice for a part-time position would, of course, be within a math department itself. For example, you could seek to be a lecturer in a math department, where you teach let's say half of the usual load, for half the salary, leaving you the other half of your time for research and paper writing. This would also give you access to professors with whom you may want to work, and you would likely be able to audit courses for free if you're already a member of the department.