Congrats on your admits!
Are you applying to the Singapore or Fonty campus for INSEAD?
I think for you it makes sense to stick with the 1-year program. LBS is very expensive. I am sorry but 2-years and opportunity cost when you can attend INSEAD, it does not seem to make all that much of sense. I also feel while LBS has London as their home turf, INSEAD is more competitive/stronger alum network.
My suggestion for you would be to start networking with students and alums now in your target industries but it will be much easier to start building your network than in 3 months. I would ping a few folks on LinkedIn from the firms you are considering (who are LBS or INSEAD or Judge or Said alums) and ask them - hey, I love the role you got after MBA, and I am in a dilemma - I have to choose between these 4 schools. if you could do it all over again and you were in my shoes, which would you pick? Get them to talk, meet them, build a relationships. Then in a few months you can always reach out about any openings they may have. If they recommend that you go to their program, they may even feel obligated to help a bit, since you took their advice. Of course they likely won't be the hiring managers and won't hire you just because you were nice on LinkedIn but this is a start of a network that will help you get a job regardless of the program you end up in.
My vote would be for INSEAD just because there is a strong Consulting culture and that will help with interview prep, though I hear you can't combine consulting and IB, so it will be impossible to recruit for both is what I heard for the US. Perhaps it is different in Europe or Asia but FYI.