I have not found a way out of the death spiral. The only current way that works are new workers. Whenever they arrive, health improves. However, the bigger the amount of workers you already have,the less role this plays. Which means that sooner or later the population will reach a critical point where deaths will be equal to those you bring with the ships.
This point should be less than the max a plantation reached and should be dependable on workload. Infrastructure should then improve this. Surely, testing will become easier once this is reached. Luckily, I have many fertile lands so available acres will not hinder my experiment.
Regarding construction, I found that easy to crack. Add 10 000 gold bars, set focus to utility and keep 15% of your total workers as laborers. Then let time flow and watch utility stars increase. Do not bother with anything else than utility till you get a high rating. What grim says about stars seems correct if you want to micromanage. Perhaps rates with fewer workers worth the micromanage. If you don't care as much for having the best rate and you keep adding workers daily, then simply follow my advice.