Post-MBA IB to SWF?

Does anyone have experience in recruiting for SWF's (Temasek, GIC, ADIA etc.) as a post-MBA Associate?

Currently a third year associate at an EB in NY, spend about half my time in TMT and the other half as a generalist. Aiming for a direct investing equity role but open to co-invest/ infra/ real estate/ credit. 

Is this transition possible? I've seen few Post MBA's make the transition but they have almost all relocated to the UAE or Singapore. NY offices seem to heavily lean the standard 2+2 kids. 

Are these firms open to networking or is it best to reach out to their internal recruiters?

Any info, advice or recruiting experiences are appreciated!