From George Washington Carver’s How the Farmer Can Save His Sweet Potatoes and Ways of Preparing them for the Table (He connected his process with starch making):
“SWEET POTATO STARCH
This is very easily made, all that is necessary is to grate the potato, the finer the better, put into a cheese cloth or thin muslin bag and dip up and down, in a vessel of water, squeezing occasionally, continue washing as long as the washings are very milky.
Allow it to settle five or six hours or until the water becomes clear, pour off; rewash the starch, which will be in the bottom of the vessel, stir up well, allow to settle again, pour off the water and let dry, keep the same as any ordinary starch.
Use exactly the same as cornstarch in cooking; I am confident you will find it superior to cornstarch; it makes a very fine quality of library paste, and has very powerful adhesive qualities.
In certain arts and trades it is almost indispensable.
SWEET POTATO SUGAR
By saving the water which the pulp was washed in first, in the starch making process and boiling down, the same as for any syrup, a very palatable, non-crystalline sugar will be the result; this sugar or syrup can be used in many ways.”
From Anoplura at ask.metafilter.com. S/he also uses shredded sweet potatoes but instead of rinsing and squeezing them in cheesecloth as Carver suggests she puts the shreds with water into a pot.
“Raw sweet potatoes have a lot of sugar, and even more starch. Cooking them activates enzymes which convert some the starch into even more sugar. You can maximize this enzyme action – and thus the amount of tasty syrup you get – by holding the temperature in the correct range (in the case of sweet potatoes it’s between 140 and 150F) for an hour. In brewing or distilling, this is called “mashing”.
If you simply want sweeter potatoes and more juice, I would cook longer at a lower temp in a covered dish. This gives the enzymes more time at the sweet spot to convert the starch to sugar, and makes the resulting juice less likely to burn.
If you want to go all out and make a pot of sweet potato syrup (which sounds delicious), you’ll need a meat or candy thermometer, some cheesecloth or fine strainer, and a pot or double boiler.
Start by shredding the raw sweet potatoes in a grater or food processor. Then toss them into a pot with just enough water to cover. Less water means better starch-to-sugar conversion. You want just enough so that it doesn’t burn. A double boiler is helpful here, if you have one.
Slowly bring the temperature up to 150F, while stirring, then cover and turn the heat off. Check on it every 10 minutes or so for an hour. Apply heat and stir whenever the temp drops below 143F.
The liquid should be noticeably sweet, and the potato shreds should be soft. Dilute the mixture with 3-4 times its volume in water. (i.e., if you have 1 pint of shredded potatoes and water, add 3-4 more pints of water.) Move to a larger pot if necessary.
Apply heat, and raise the temperature to 170F, stirring as you go. This will stop the enzyme action, and start to free the sugars trapped in the shredded potatoes. Once you hit 170F, turn off the heat. Strain the shreds out of the liquid by pouring it through a strainer or cheesecloth.
You will now have a tasty, but dilute sweet potato syrup. You want to reduce this by half, or even 2/3rds to make a thick syrup. A double-boiler or slow-cooker is strongly recommended here. (you don’t want to waste an hour-plus of work by burning it!) Go slow, and check the viscosity regularly with a metal spoon. Take a small sample and let it cool to see how thick it is at room temp.
Note that the above instructions will also work with pumpkins and most other types of squash, except that most of them don’t have enough naturally-occurring enzymes to convert their own starches to sugar. To accommodate this, you need to crush up a tablet of Beano and mix it into the shreds in the “mash” step.