I tried this many years ago ... don't remember success but ...
the coarse rid model will give you displacements at the nodes (Duh) ... I think the key is on the fine grid model enforce a linear variation of displacement (so the fine grids between the displaced coarse grids see their respective displacements. model a simple panel first ... uniform stress applied to the coarse grid, displacements onto the fine grid ... do you get the right stress ? then a linear varying stress, then a couple point loads (complex displacements), then you should be ok with your real model.
these days you might get the desired effect using RBEs around the perimeter.
of course you can always transition mesh the coarse grid model ... but that could have problems of it's own (surface loads ?)
another day in paradise, or is paradise one day closer ?