Hello Megan,
I've just been through a move and had similar thoughts on moving plants. I decided to not try digging anything out, although I took some cuttings. If you take a lot of the plants, the garden will be a bit of a mess. In the end I resigned myself that perhaps the garden would be like leaving a bit of an echo. I know a young family moved in, and perhaps in a few years we will sprout a new permi here?
Secondly, this is a real opportunity to start over and avoid some mistakes that were just too much work to overcome in your old place. Make a truly spectacular garden. You might have to learn how to fit in with the new environment. Did you move far enough to change Ag Zone? Change soil type? If so you will have lots of fun making a whole new set of mistakes!
Over the years of wandering, I've left fruit trees, asparagus (why do they take 3 years to start yielding and my jobs would only average around 3 years?), raised beds and trellis in my wake.
Good luck!