The endurance of borders and the nation states they seal is an issue of cultural and political inertia, much more than an issue of finding the optimal economic policy to allow them to open up.
Frankly, and somewhat sadly I might add, I think even if you somehow proved - proved - to a nation's voting population that they would be better off economically (in aggregate) by opening their borders, the perceived cultural and political effects of such a policy would prevent it from ever passing into law through any democratic process. Culture and politics are intertwined in a feedback loop, and it will take many more generations to have grown up in the globalised, internet and cheap-air-travel connected world, where almost every person interacts with, makes friends with, works and does business with people all over the world, for this default to finally go away - only when it does can we ever hope for an open borders policy to even be a remote possibility politically.
With that said, I think aiming directly for an open borders policy might be missing the wood for the trees slightly. Might I instead suggest that we pile research resources and efforts into things like better remote working technology, practices and protocol that might eliminate many of the problems (certainly not all - and mostly economic - but many) that an open border policy should aim to solve in the first place?
In my view the world would be a much better place if we did simply have an open-borders policy throughout much of it, but we can get a very long way towards that goal by allowing people to work from anywhere, for anyone, in a completely effective manner. Not only will this actually solve some of the problems that you talk about a lot more quickly and easily, it should have the effect of flattening out the global distribution of wealth somewhat, such that open borders actually do become more palatable politically, simply because the figurative pressure on the borders of the wealthiest nations would be reduced significantly.
In other words, open borders is not something that can ever happen all at once as a result of a policy change. No matter how much research we do into those policies, they just won't succeed politically as a step change. Rather, it's a positive feedback loop of gradual cultural and political change that has to start somewhere. In many ways of course it's already begun, because of the internet, and I believe the next stage to chase is better, really effective, remote working. I think that's where research effort towards the solving the problems you talk about would be most effectively invested.