Law Degree over MBA in Turnaround/Restructuring Consulting?

I haven't been able to find too much information online about JDs in M&A or restructuring consulting, so I thought I would try posting here.

I started working in audit at a large mid-tier firm (BDO, RSM, GT) fall 2017 and left right after I made senior for a senior TAS role at a smaller (top 10ish) middle market accounting firm. I've been in my role a little over a year and I'm thinking about going back to school but I'm not sure. 

I audited some BDCs and PE funds that focused on investing in distressed companies, and while I hated audit, I became really interested in working with distressed companies. I applied to some restructuring firms as an FSO audit senior with a CPA but unfortunately couldn't land get any interviews. My TAS role now is a lot of FDD, but since the advisory practice is smaller and less structured than other firms I've gotten a lot of other M&A consulting and some valuations experience. 

I would really like to break into a firm like Alix, FTI, or A&M but I'm unsure of the best way. I went to a large well-known state school on a full ride, had a high GPA and finished with a BS in accounting and a finance minor. I'm thinking that getting another degree from a prestigious school might be the best way for me to break into the restructuring space, but I don't really want to get an MBA. I understand the value of MBAs are in the network you build and not the courses, but there's nothing that excites me about MBA curriculums. Going to law school and focusing on corporate transactions and bankruptcy law seems like it would be really interesting and helpful, but I've only met or read about CPA/JDs who work in tax. 

Any advice or information about law degrees in turnaround/restructuring consulting, or consulting in general, is greatly appreciated.

tl;dr - went to state school, was in audit, now in TAS, want to be in restructuring/turnaround, don't want an MBA, would a law degree help me?