How do get the "caramelized juices" from yams

It seems that the best answer to your needs will be making a treacle. It may be challenging to do it with yams, it's typically done with less starchy plants. But I don't think it's impossible, it should be worth a try.

Making a treacle basically involves taking a fruit juice, and slowly evaporating and caramelizing it. So, your first step will be to somehow juice the raw yams. Treacles are messy to make and lots of effort, so if you don't already own a juicer, it's probably better to not get one until you've done it a few times and are committed to continue. Especially seeing that it might turn out to not work well with yams. You could ask somebody to loan you a juicer (many people don't use theirs), or, if you can't find any, use the old method of pureeing the yams and then pressing them through a cheesecloth. Adding a bit of sugar should help both the juice flow and the later caramelization.

In the second step, you reduce the juice to a treacle. For that, pour the juice into a wide pan or pot. Place it on a very low flame, so low that it doesn't even simmer (but it should be hot, not just warm). Leave it there for as long as it needs, controlling it occasionally and giving it a stir. It's ready when it has the consistency of uncrystalized honey. It'll take many hours to reach that stage, but be aware that, with the hob set to the same setting, the liquid will get hotter towards the end after most of it has evaporated. So, in the final stage, you have to monitor it constantly (and also reduce the temperature a bit), or you will end up with sticky charcoal, and might even ruin a sensitive pan coating such as PTFE. (It's probably best to do this in a thick bottomed stainless steel pot/pan).

A properly reduced treacle is shelf stable, like jam. It can be used in most places where people use jams, honey, or strong syrups like maple syrup or sugar beet syrup.

It might be possible to roast yams, whip them up and the spin them in a centrifuge. I imagine the yield would be incredibly low because the liquid content of a yam is fairly low. What if, instead, you attempted a yam flavored syrup? You could roast cut up yams in a simple syrup, mash/whip, then clarify. Again, a centrifuge would be ideal, but there are other methods, like agar clarification, which can be accomplished at home.