And here's a picture of the plant 1 month ago just after I brought it home.

Looks like it's not getting enough light. Do you see any root nubs on the stem of the longer part yet?

Hmm, I have it on the top shelf in an open area with windows on three sides, but it is about 6-10 feet away from the windows, depending on the window. It gets a short bit of direct morning sunlight at this time of year. I'm limited as to where I can put it.

I'm not sure what the root nubs would look like, however on the main stem there is a small offshoot and another which appears to be coming from the soil very close to the stem.
(see attached pic)

That is likely too far away for decent plant growth as born out by how stretched out (etiolated) the plant appears to be. Two things to keep in mind when contemplating light:
1) The amount of light a plant needs for photosynthesis is FAR greater than our eyes need by which to see. Just because an area seems plenty bright to our eyes, doesn't mean it is enough light to meet a plant's needs.
2) Light intensity falls off rapidly the further away you are from the source. It follows what is known as the invenvers square law -- the intensity of the light falls off with the square of the distance one is from the light source. So if we assume the light right at the window is "the source" (and therefore strongest), if you plant is 6ft away from the window it is only receiving 1/36 of the light it would have received right by the window. If the plant is 10ft away, it is only receiving 1/100 the amount of light.

Thanks for the explanation. I am aware that to a plant it's not always as bright as it is to us, but it sounds worse than I was aware. I really wish I had more locations near windows I could put them, but that's just not possible.

Most of my plants are doing well on the multi-level shelves where this plant is located, though I'm noticing a few, such as this one we are discussing, are clearly wanting more light.

So, does anyone know about propagation?

Can I chop off the tall pieces and stick them back in to the pot and start new plants?

Should they be cut at any specific spot?
Should they be rooted in water or in a separate pot so watering can be controlled differently vs. having them planted back with the parent plant?

I was reminded of this plant again today when I noticed it has grown another couple of inches! :)

I've not tried propagating pieces that didn't have aerial root nubs yet. I don't see any on your plant, but if you pull the brown bits of lost leaves off (in the last pic,) you'll be able to see them when they start, you may see bumps under the brown bits now. If there's not enough light for the mama to grow correctly, I don't think you'd have great results trying to propagate right now. Doing it outside in the humidity of summer would be the best thing to try.

I agree, your plant looks like it's reaching for light, it could/should be standing up straight, eventually developing a trunk appearance though I haven't left my plant(s) alone long enough to know if the stem actually lignifies with age. This plant is not a creeper. Are you able to offer more light by putting plants outside for summer? You wouldn't want to put this in direct sun, except maybe the first or last hour of the day, but the shade outside is infinitely brighter than inside.

Try a grow light they sell cheap ones on Amazon I paid $15 for mine!

Sorry not the best picture

It seems to be a weed in the tropics. Here are several growing in cracks of stone walls at a resort in Cancun without much ado. It looks like they like the sun and drier conditions to do well?

Beautiful! I have taken pics of them in FL in similar locations. The plant in the pic I added yesterday has been kept in much lower light. It takes too long for me to bother continuing to acclimate to significant exposure when they have to come inside for winter. No doubt they are more upright and colorful that way.

My same plant in 2013:

https://garden.org/plants/photo/213141/