Feeling out of my depth - 1st year analyst at a lmm repe interviewing with a global investment manager

I am an analyst at a local LLM value-add REPE shop (~300m AUM) and I've been with the company for roughly 9 months as of March. I'm currently the shop's only acq analyst and we stick to deals in my local area. While work has been solid, I am aware that the learning curve at these specific shops doesn't require much technical knowledge and reps have recently slowed to snail pace. Since the new year, I've become a little... bored in my role and the lack of cohesion in day to day operations isn't helping me build good habits.  Due to the shop's rapid scaling over a three year period, operations are a mess and require constant attention, taking way attention from my role and leading to many days were I am swamped in projects that don't relate to the role I'm employed under.  

A week or so ago I submitted an app (via LinkedIn) to a firm that I've been familiar with for a couple year. The role is on an acq/dev team and although I don't have development experience, my current analyst role matched the responsibilities on the listing, so I figured this could be a good exit opportunity from my current job. 

After getting a call back and getting through the screening call, I received an invitation to a second, in-person, interview at the investment firm's regional office and a take home case study. 

As I have prepared for this second stage of the recruiting process, I've received help from a couple friends who work at the institutional level. While I'm confident in my ability to model, I believe the small shop style has rubbed off on me, as talking to them and hearing their investment thesis and strategy felt like we were discusses two completely different fields of work. The structure, wording, sophistication, all gave me a slight panic. 

Maybe it's specific to the type of asset I specialize in, or maybe it's the small shop style of uw and flexibility, but the step up from small shop to global firm seems intimidating. While I feel confident I can be prepared for a number of different scenarios during the recruiting process, I feel like my lack of institutional background is not going to help my case. 

Has anyone made a similar jump, and if so, how did you showcase your strengths to such a firm?