Why not carefully transplant the entire thing now? What I would do is dig a hole large enough for the entire tote, take a sharp knife and cut along the bottom but keep it in place. Maybe cut a section then tape it with some duct tape, work your way around till the entire bottom is cut free. Place the entire thing in the hole, cut the tape and slide the plastic bottom out from under the tote so the root ball(what there is of it now) is sitting in the hole. Now cut the sides off and slide them up as you fill in the hole. water the ball sufficiently to fill any voids and settle the soil around the plants.

I think is you do this very carefully the plants should be fine. If you wait till next year to transplant them your pushing any harvest back another year.

For future reference, Asparagus should be planted in a trench 10-12 inches below final grade, covered by an inch of soil. Water regularly and watch for growth. Keep covering the new shoots with more soil as they grow. Continue adding soil until you have filled the trench to match the final grade of you bed.

I just planted my first bed this spring too. Though I made a raised bed for mine by digging 6 inches deep and building up the bed with 2 layers concrete retaining wall stones so it's now about 8 inches above the surrounding grade.