Upfront let me say I know very little of LVDTs and have never used them, but they are a very elegant way of sensing linear displacement.
When you say they are inherently frictionless....although simple, they have moving parts so there must be some friction? And in wet/icy conditions they could get frozen?
Were I to encounter the problems of crosstalk I would try something like using different excitation frequencies for each LVDT, and have a narrowband filter in each signal conditioner. Are solutions like this used? But Alliance's solution is also clever. And I suspect thay know more than me about these things :-)