This symptom does not suggest late blight, but might indicate a stem borer or some type of crown rot due to crowding or excessive moisture. You can cut into any discolored or mushy/collapsed stems to look for indications of a boring larva. If not readily apparent itself, its frass (excrement, which will usually look like dark pellets) should be evident within a hollowed-out stem.

Do you know about how often the plants are being watered? That is, are they being allowed to dry somewhat in the top couple or so inches of soil before being watered again? Is the straw piled up against or touching the main stems? (If so, can it be pulled aside a couple inches to allow for better airflow to reduce the risk of fungal infection?)

If you aren't certain about the stem symptoms and any presence of a borer, feel free to send additional close-up photos of the stem damage and wilted sections. (Ideally a file size over 1MB for each photo, since that lets us zoom-in if needed; we can't zoom-in on the current photos to see more detail.)

Miri