PE BD -> IB -> PE Deal Execution Side?

Dear WSO-Community,

I very much would like to get your advice on my situation:

I have been in PE/growth equity for about 2.5 years at this point; the first half year in a deal execution role, the second two years in a business development function i.e. sourcing and analyzing deals. Over the last year, I have become continuously more frustrated with my BD role as I would like to “see things through” and not hand over an investment lead to the deal team and then step away from it and never see it again (or eventually see it again when the deal closes). Hence, I have a strong desire to get back to the deal execution side.

Taking a step back: I am an immigrant from Germany. I started a Master’s program in Germany, had a 1-year study abroad-stint at Tulane University (partner school of my German university; other partner schools include Booth, Stern, Dartmouth, and Emory, just to give you an idea), met my back-then-girlfriend-now-wife, graduated from my program with an MSc in Finance, moved to LA, and pretty much right as my work permit/Green Card came in the mail I had managed to network myself into a PE/growth equity-startup backed by two asset management firms and founded by a few fairly experienced tech-PE guys from a couple of renown MM PE firms.
As I had mentioned, the first half year I pretty much did everything from building financial models to commercial due diligence to investor relations to deal sourcing. As the team grew, there was a need for more deal flow. Since I was the most junior guy, and also the one without any formal IB or consulting training, I became the BD-guy.
As I had mentioned, I grew to be fairly frustrated with the role and would very much like to move back to the deal execution side, however, at my current firm that’s not going to happen (in case you are wondering, I already had that conversation with my colleagues). Naturally, I began to check what else was out there. However, after a few recruiter conversations, it became pretty clear to me that without any formal training, ideally IB, being on the deal execution side was not going to happen by switching firms.

Now, I see myself with two options: (1) continue in PE BD at current firm, perhaps switch firms and continue in BD (and remain frustrated) or (2) leave PE, find an IB-Analyst-Program that will have me, put in the work and learn the hard skills from scratch, then, after 2-3 years, try to get back into PE or growth equity.
I am on board with option (2), yet I am unsure which (legit) IB’s recruiting profile I am going to fit into. I am 32 now and have been out of school since 2016. Prior to my MSc I had my own dietary supplement startup, interned at three tech companies, and prior to/during college helped my dad turn around an unprofitable SME (this was all in Germany).

I always liked numbers but it wasn’t unit later in my MSc program that I realized that the investment world was the place where I wanted to be. In a way, I had a lot of luck landing in this industry right out of graduate school, however, right now I feel like I am stuck in a dead-end street. I know, a bit of an odd story. Nevertheless, any advice is greatly appreciated!

Thank you and all the best!