Capital Markets Advisory to IB Lateral?

I'm currently a capital markets advisory analyst at a smaller firm (<200 employees) and I'm wanting to lateral into IB at some point in the near future. The firm and its competitors are definitely more "Consulting" (as per my profile) rather than a bank. Our primary strengths are M&A, Investor Relations, Activism Defense, and really anything public-facing that falls under the purview of a CFO. The work is pretty high level as we work with C-Suite execs and boards. Our clients tend to be mid and large-cap public companies with the occasional mega-cap and pre-IPO. 

Came from a low semi-target school and graduated with a 3.7. We have a little OCR and a solid network. A decent number of my peers managed to get IB in BB and MM but I was unable to due to being late to the recruiting cycle (didn't get serious until Jan/Feb). My technicals are strong but I got dinged from my 2 interviews likely due to fit and no SA experience. As a result, I settled for this job. 

I figured this is close enough to IB and high-level enough to where it can be transferable. The culture is great and the comp is solid (market rate for non-MBB consulting). Most of our senior folks are laterals from IB, ER, Buysiders, and Corp Fin so it does seem reasonable that the reverse could be possible. 

It's a bit of a niche subject but I'm hoping anyone can provide some insight into if this is a possibility or how I ought to go about it. Thank you