Fran there is/was something available called Vilene Fusible Bias Edge Tape - use this tape anywhere that is prone to stretch, shoulder seams, necklines and armholes for example. Ensure that the stitch line of the tape sits on the seam line, widest side to the edge. Use a dry iron, wool setting for six seconds to ensure bonding. Stretch slightly to ease garment on to tape as you press. This information came from Janet Molville when she was writing for Sewing World, so is a good few years ago now. This tape was available in white or charcoal and you could buy by the metre.
However I also have in my stash something else by Vilene called Edge Tape, this is an iron on stitch reinforced tape and came on a roll of 20m x 2cm. in a poly bag with an instruction sheet.
Lastly I have some Vlieseline bias tape T12, 12mm x 5m comes in white and charcoal - this I obtained via Amazon when I couldn't put my hands on the tapes above, and of course as soon as it arrived I found the original tapes - isn't that always the way. I also sent up some of this Vlieseline bias tape to Bodgetandscarper when she was making her 'mother of the bridegroom dress' as time was crucial.
I believe the huge angle of the front of wrap bodices have a nasty tendency to stretch however careful you are, and if you can get some of this bias tape and adhere this to the neckline before you move the freshly cut piece off the cutting table then you might be lucky and not get any stretch, you have nothing to lose from this.
So far you bodice is looking good, and as you say the weight of the skirt could make it pull down, if you do not want this to happen then making a waist stay would be a good idea. Love the colour and pattern of your fabric choice, should look stunning when finished.
Another tip I learned from one of my bosses many, many years ago, was to sew the middle of a piece of elastic in the middle of the bodice underneath, i.e. the wrong side of the bodice, and then take this elastic around your body and fasten at the back - this then stops the front of your bodice falling away from your body should you lean forward. Another way you can do this but on a different style front, is to cover a piece of lightweight boning in lining fabric and attach strategically to the underside of the front of your bodice but just high enough that this piece of boning can be tucked inside your bra and again this stops everything from flopping forward.