What I would do is root cuttings. Take a small handful of damp LFS and wrap it around the stem where you can see the nodes and wrap that with plastic. Keep the LFS just damp not wet and when you see roots developing you can cut the stem below them and pot it up. You could make 2-3 new plants from that one and the original should send another growth point up from the root.
There are other ways of doing it but this technique is the safest way to guarantee roots instead of rot. I'll see if I can find a link to a tutorial on this technique for you.

Taz' suggestion is interesting. I think I'll try that on one or two of mine.

The other option is simply to wait. Generally, after my Neps send up a long leafless stem like in your pictures, they tend to start some new leaf growth at the base of the plant. The new leaf growth generally makes pitchers quickly, and then you have a couple of growth points, rather than one.

That's one possible solution, but it's actually called air layering. Root-cuttings are when you cut off pieces of root and plant them directly in soil (works w/ sundews, never w/ Neps.) The downside is that layering can be a pretty complex process, and you do risk killing your plant.

There's nothing wrong with just transplanting your plant as it is. You can bury it a little deeper if you have a bigger pot, and that shouldn't cause any problems.

Your plant (it's very nice, btw) should eventually sprout a new basal-offshoot. If you haven't experienced this before, it's when a dormant node below the soil activates and sprouts a new stem.

Once the new growth point is well established it's much less risky to experiment with layering or taking cuttings from the old growth-tip.

You can encourage new basal-offshoots by bending or tying-down the stem so that the growth point is below the root-ball. This signals to the plant that its vine has fallen, and it's time to start a new one.

I meant root cuttings as in the action of rooting cuttings not rhizome cuttings (funny how others can tell you what you mean)and yes the technique I described is called air layering. It's not as risky as rooting cuttings when you only have one growth point.
Transplanting the way it is can be risky too. If you were to break the stem in the process you could lose the whole plant or it could send up a new growth point. If you do break the stem while transplanting then keep it on the dry side and it should send up a new growth.