Hi lawyer,
I was on the waitlist for this year's intake but asked them to be considered for nex years 2021 intake due to personal reasons and the Corona thing... They made an exception but it worked.
In terms of converting, I sent them an update in the beginning of January with a promotion, added responsibilities on projects and my plan for the year. I also had a short interview with the waitlist coordinator (which was probably helpful because I bombed my admissions interview).
Around May I provided an additional letter of recommendation from a client.
Since I wanted to expand my option field, I also retook the GMAT and provided them with an updated score (700->750) right before their waitlist decision in September. In the mail I also told them that I changed my post mba career goal from a move to VC to staying with my MBB.
Hope this helps - might be quite specific to my application but maybe you can use aspects of it
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