I wouldn't move it now. By moving it, you automatically damage the roots, and with summer just around the corner, the damaged roots will prevent it from absorbing enough water for its needs. Until they recover wilted leaves and dying branches would be the norm at this time of year, with a possibility of the plant not recovering, but dead instead.

Since Jane is a deciduous Magnolia, I would move it in the late fall after it's leaves have dropped. Check it throughout the winter to make sure our winds haven't dried out the soil or plant. If the disturbance wasn't too great you may have a complete show next spring (spring weather permitting)

As for now, you can probably prop up the branches that are going sideways with a pole and rope/wire. If that isn't successful, you could always prune to a pleasing shape after you transplant it, it will respond by budding back along the cut branches, and in a year or so you will never know that it was pruned at all.

FWIW - I have a Jane Magnolia in my yard, and I have to prune out low branches every few years, so it doesn't hide the perennials underneath.

I second that vote.
LAst memorial day (memorial day is this w/e) was when we began to see really hot scorching temps in the 90's and very dry weather. According tothe weather man on TV, we are looking at having another awful summer like last year with above normal temperatures and very dry. If you haven't done what you were wanting to do in the garden by now then it's probably just too late.