Plant Parent
This plant has gotten so leggy! I’m not sure if I should cut it all off to propagate the pieces, repot it, etc.

The overall plant (vines in normal resting position):

Darryl
Thanks for submitting your photos and care details!
Growth Structure:
It is totally normal for this Peperomia to grow too tall to stand on its own – to the point where the stems flop over. If you want the compact look of a “new” plant, then you need to take cuttings and replant them into new soil. Here’s a diagram from my book ‘The New Plant Collector‘ showing how the life cycle progresses – and where your plant is now:

Poor Soil Condition:
In terms of the overall health of your plant, your soil is probably quite compacted and has mineral accumulation – which I think explains why you have several dead stems. Whenever you plant into a pot without drainage holes, while it isn’t an immediate death sentence, you need to be aware that there will be no place for minerals to be flushed out, which is why changing the soil in good time is critical – 1 or 2 years maximum for a small pot (less than 8″ in diameter).
Example from My Collection:
Here’s my plant after 3 years of growth (it had drainage holes and I used a 3-1-2 fertilizer) – notice the foliage all the way down the long stem:

And another 4 years later (7 years total), the original stems have flopped over (I didn’t bother to stake them up) but new pups were emerging from the pot:

In hindsight, I should have taken cuttings once the stems grew past 8-10 inches tall to keep the overall plant looking nice and compact.
Recommendations:
At this point in your plant’s life cycle, I think you should take cuttings from all the healthy stems. Place the cut ends in water, which should encourage roots to grow. Once the roots are about an inch long, pot them into good potting soil (peat moss, coco coir, and perlite – which is most soil labeled “indoor plant soil”) and use a plastic nursery pot that has drainage holes. You can place the nursery pot into a decorative container that doesn’t have drainage holes – this is how I prefer to pot up most of my houseplants because it allows me to occasionally take the plant to the sink to give it a thorough watering, ensuring that all parts of the soil are moistened. Dry pockets that form with “patchy” watering will kill off some roots and, eventually, their corresponding stems.