Moving to education sector banking before moving to education sector VC/PE

Hi everyone. Question bolded below if you want to skip the background.

I majored in education at a target school and currently work at a Tier 2 consulting firm in an education practice that does 80% due diligence for PE firms and 20% corporate work (usually growth strategy for PE portfolio companies following deal close).

I am looking to move to an education-sector PE or VC fund. I have networked with 5+ ed VCs and 5+ ed PEs that have various recruitment processes.

I am starting to see that even with my education background, investment banking experience is highly valued.

Question: Would it make sense for me to move from consulting to an education banking group such as Macquarie's education group, JPMC's higher education group, or Goldman's education technology & knowledge services group before moving to education VC/PE?

Pros: Get further deal and modeling experience in the IB context. Financial experience to round out my operational/strategic/market experience doing consulting due diligences.

Cons: Look like a total job-hopper opportunistic career climber if I move from consulting to banking after 1y, and then try to move shortly thereafter to VC/PE. I am worried that I will burn bridges with my dozen or so contacts at education PE/VC funds if they think this move is shitty.

What do you think? Thanks for the help.