Please evaluate my strategy on how to lateral to McK or BCG.

Major question in bold

I currently work at a T2 boutique (LEK, OW, S&, Parthenon, ATK, etc.)

I do private equity due diligence for a specific sector. I studied that sector in college.

I have been there just under 1 year and since I started out specialized by request due to interest in the sector, I have gotten to take on a senior associate role very quickly (if structure is associate, senior associate, manager). I own both qualitative and quantitative workstreams and manage junior resources.

I am pretty burned out of DDs. I am routinely working 80+ hours per week and want to just do sector work at McKinsey or BCG who have top notch practices that do non-profit, governmental, and commercial work in my sector.

1. I plan on emailing 4-5 partners / principals a week asking to talk about their work to get them on the phone (I'm not bad at this step and probably get a 20% conversion rate).

2. Once I get them to agree, I will do thorough DD on their work as possible and really impress on the call (confident in ability to do this)

3. Once I call, I will ask them if they are aware of the experienced hire situation (is this too direct? should I not ask about hiring?)

4. Now what? How do I convert this to an interview? How will they respond to me asking about experienced hire situation? Should I phrase differently?

5. Crush interview

Where am I missing steps? What could go wrong with this plan?