Thanks for clarifying (I am sighing in relief because that's what I thought you meant and I didn't want to butt in later.
))
My garden is a little cooler than yours, I expect. My asparagus starts to emerge in April, I think.
What is your window for being able to move it? Only around move time? If so, I think I would let all the stalks grow until time to move, then cut them off, dig, move it.
I'm not sure the work will be worth it. And you'll be pretty busy at moving time. But
Doing it right now, I think is better, if possible.