Turns out in unity the mesh morphing just straight out WORKS with no real effort. It's only a skinned mesh, which is the same sort of thing you'd be doing with skeletal animation. In UE4 (the other potential engine, and in fact most likely engine) it almost works straight off, with just some minor work to tell it that the crazy bone structure we use is OK.
Porting wise it's basically grabbing the entire "game" which is made of LUA scripts, then getting the new engine to sit under all that pretending to be the old engine. I would quite honestly expect that to take 8 months at the very least, but that's OK as it'll be during a phase where we'll also be adding content and doing the massive testing and balancing task of the tycoon game, which will take ages and will be artist and designer heavy, but not very programmer heavy.
If you're worried this will cause the project not to be finished, don't be.
If you're worried it'll cause it to take longer, well that's entirely possible, but for the long term future of the game I think it's worth it. And we've never been about getting things out in a rush compared to getting them right.
*Disclaimer: this is my dumb artist understanding. Programmer could tell you more, but our plan has been checked for sanity, don't you worry
