If your standard seating stem left a ring on the bullet nose, chances are good the cavity was already sufficiently long for the Hornady A-tips. The problem with using a standard seating stem with VLD bullets is typically that if the bullet meplat actually "bottoms out" in the cavity, meaning the stem is actually seating the bullet by pushing it in from the nose, then the nose of the VLD bullet is simply too long for the cavity in that particular seating die stem. For that reason, the cavity in VLD seater stems is typically much deeper. However, the bevel inside the mouth of the stem may also be ground at a steeper angle more suitable for contacting the ogive of VLD (secant ogive) bullets. Using a standard seating die stem with a VLD bullet that has too long of a nose will generally not leave a concentric ring around the bullet nose, as the bullet meplat "bottoms out" in the stem cavity and actually prevents the bullet ogive from ever appropriately contacting the beveled surface inside the mouth of the stem.
If you haven't already done so, you can easily check your standard seating die stem to determine if the cavity is deep enough for the A-tip bullets using a toothpick (or similar). Push an A-tip bullet as far into the stem as you can, then mark a ring around the ogive with a sharpie. Repeat that process with a toothpick that can be pushed all the way to the bottom of the seater stem cavity. Then compare the lengths of the bullet meplat to the mark, and the toothpick tip to the mark to determine whether the nose is too long. If not, you may just need to use a little steel wool to smooth out the inside of the standard stem that was originally causing the ring around the bullet ogive. I mention this solely because it sounds as though you didn't have the problem with the bullets sticking when you were using the standard stem. As I described above, the ring caused around the meplat does not necessarily mean the meplat of the A-tip was "bottoming out" in the standard seater stem cavity.
There may be a different reason that your A-tips are becoming "stuck" in the VLD seater stem. If the beveled mouth and interior of the VLD stem are a very good fit for the nose of the A-tips, it may be that they are generating a vacuum behind the bullet nose when pushed into the stem, i.e. forcing out some air, forming a tight seal, and then becoming stuck. You might try chucking up both stems in a drill, and running them over a small piece of steel wool you have compressed to fit tightly into their respective cavities. In the case of the VLD stem, this might scuff up the inner bevel to prevent a vacuum from forming. In the case of the original standard stem, it can smooth out the bevel sufficiently that it won't cause a ring around the bullet nose.
Finally, doesn't Hornady recommend using a special seating die stem for their A-tip bullets? I understand those may not work with your Wilson die, but there's probably a good reason Hornady made that recommendation. It might also be worth giving them a call to see if they have any other suggestions worth trying in your specific situation.