William Whitson

As others have said, the problem is virtually certain to be late blight, one of the most common potato problems.  The good news is that you have lots of options since it is one of the most common problems.  The bad news is that it remains one of the most common problems because none of the options are perfect.  You can do one or more of the following:

* Grow late blight resistant varieties.

No variety has durable resistance against late blight, but many have adequate resistance to get a crop, particularly if the strains present in your garden have not cracked all the resistance genes.  Modern, commercial varieties are more likely to have useful resistance than heirloom types.

* Time your plantings to avoid blight weather.

Blight is most likely to occur when the weather is cool and humid and it takes some time to develop in areas with cold winters, so you can grow early varieties earlier in the year to try to bring in a harvest before blight occurs.  Also, late varieties have a certain degree of innate resistance because they remain in a active growth phase during the period of time when blight tends to be most active.  Depending on the strains present in your area, you might find that late varieties will still produce a reasonable yield even when infected by blight.

* Use fungicide.

There are both Organic approved (but still fairly toxic) copper fungicides and non-Organic fungicides.  The copper fungicides are only effective when used prophylactically - you have to apply them before blight arrives and keep applying them after rains.  They are not very effective, but are often enough to get the plants to harvest.  The non-organic fungicides tend to be pretty effective - enough for commercial agriculture - but I don't have any direct experience with them to offer.

It is also quite possible that you will not have blight the next time that you grow.  Blight spores blow on the wind, often from miles away.  If the weather is different, the wind comes from a different direction, or your neighbors grow different plants, blight might not arrive in your garden or might arrive at a time of the year when it is less damaging.  You will want to remove any volunteer potatoes from the previous year since they can carry over blight and start the infection again.

Nick Kitchener wrote:https://laidbackgardener.blog/2020/04/05/determinate-and-indeterminate-potatoes/

It is always interesting to see someone go to the effort of writing a very authoritative looking blog post that is pretty much total fantasy.  The author could not have actually tried growing determinate and indeterminate potatoes to arrive at these conclusions.  There are virtually no important distinctions between determinate and indeterminate potatoes to the casual potato grower other than that determinate potatoes are early to mid season and indeterminate potatoes are late.

As for the original topic, there are a lot of reasons why growing potatoes through harsh conditions is not ideal.  An early start is one thing, but when you make tubers that have ended their dormancy wait for months before they can put on normal growth, all kinds of wacky things can happen.  What you are doing in terms of potato biology is manipulating the physiological age of the tubers, which is essentially the biochemical clock that determines how a potato plant grows from a tuber.  Potatoes that are stored well, free of disease, and not held too long before planting have low physiogical age and they retain apical dominance (they form fewer stems) and grow longer before initiating tuberization.  This gives you a later but larger yield of tubers.  Potatoes that are stored under poor conditions, have heavy viral loads, or have to wait a long time before being given the proper conditions to grow lose their apical dominance, form lots of stems (assuming a large seed piece with many eyes), and race to tuberization, forming more but smaller tubers and lower total yields.  You can game this system to some degree as you have done in this case to get plants to race out of the gate in the spring and give you an early crop, but you could largely achieve the same thing by chitting tubers so that they are ready to plant a month before your last frost.  This avoids all the potential problems of growing in cold soil, including things like bacterial and fungal infections resulting from the cold sweetening of the tuber or little potato syndrome, where th plant goes into full emergency mode and just uses the energy in the tuber to form a bunch of little tubers and never makes a plant.

Logs certainly level more easily than blocks, but as long as the beds aren't really long, it isn't too hard to level them.  If you plan to make a lot, you can have somebody come in and level with a tractor bucket.  If it is just a few, I find that a grub hoe is the best tool for the job.

More about my experience with block beds here:
https://www.cultivariable.com/how-i-build-raised-beds/

Artificial light is generally not sufficient to increase glycoalkaloid content in tubers.  The sprouts can have very high glycoalkaloid content, but the tubers are still safe as long as the sprouts are removed.  There are actually a lot of factors that contribute to glycoalkaloid intensification, including long storage and storage at warmer temperatures, so potatoes do tend to become more toxic over time, even if kept out of sunlight.  You should be able to taste bitterness in tubers that have become unsafe to eat.  The safety limit for glycoalkaloids is 20mg / 100 g of tuber and most people perceive bitterness starting somewhere between 10 and 13 mg /100 g, so you would be likely to notice before the potatoes become dangerous.  Of course, some people are insensitive to bitter flavors, but you would probably know if that is the case for you.

I generally cut off the distal end of the tuber and then plant the rest of the tuber in soil in a shallow nursery tray.  Cutting the end off breaks apical dominance so that the remaining eyes will sprout.  You can jam the tray full of as many tubers as you can fit.  When the sprouts start to emerge, you just detach them from the tuber and you will have a small plant that has already rooted.  The tuber will keep sending up sprouts as long as it has eyes that haven't sprouted yet.  You can easily get a couple hundred sprouts from a packed tray.

Looks like Septoria.

Potato stems will root very easily as long as you take them before flowering/tuber induction.  You will get a single stemmed plant that will have a smaller yield than a multi-stemmed plant started from a tuber.

Solanaceae are really vulnerable to broad leaf herbicides.  Around here, it is nearly impossible to find manure, compost, or straw that is not herbicide contaminated.  I don't bring anything on site anymore unless I can leave it to compost down for three years.

It won't be a problem for long unless you kill that coon or improve your enclosure.  Once they get into poultry, they come back night after night.  So, I'd say job #1 is figure out how to protect your duck.  Finding it some friends is also important, but not as urgent.  Ideally, you would just get a few more ducklings.

Even if another duck takes in your duckling, there is no guarantee that the duckling will not return home to seek you.  We had a sick duckling that stayed inside with our dog for a few days while recovering.  After that, it would go hang out with its siblings, but only while the dog was in sight.  If the dog went away, it would try to find her.