Hi, just my two cents.
Firstly, impressive list of achievements! Definitely achievements that would be attractive to the very best law firms
Secondly, I really do not think you *need* legal experience to get a TC and definitely wouldn't need that to get a VS offer. I have attended so many law firm events where lawyers/grad rec reiterate the fact that they know getting legal experience is difficult. What they look for is a manifest interest in commercial law and sharp intellect (through good grades, which you clearly demonstrate).
To demonstrate an interest in commercial law, what I did was to attend a bunch of insight events. I think I attended about 20 events the past two years. Look to apply for competitive insight days as well. I also completed forage internships. This was enough to get me a TC interview invite at
Slaughter and May. I had not done a VS before this interview. Of course, it is important to be able to speak about what you learned from these and how they reinforced your interest in commercial law.
Secondly, I think you should be able to show transferable skills. i.e.:how are the things you have already accomplished relevant to law/ how would they make you a good lawyer? In doing this, you would show that you actually know the role of a lawyer and have thought deeply about it- making it clear that this new career trajectory isn't just a whim which can easily change.
There are lots of interconnections between law and economics and so I do think it would be quite easy to come up with a compelling 'why law?' response which shows clear reasoning.
I hope this is useful. Goodluck!
(I also came from a quasi-economics background and have now gotten MC offers this cycle, so just know this is very doable!).