STEM / research jobs and certain niche fields like "high finance" and corporate law. Basically all the things that require a huge investment of time and money to be qualified for... except the education system should make it easier / cheaper for Americans to obtain those credentials versus their counterparts abroad.

Americans should be inventing the machines to replace workers abroad, not competing to be a Foxconn factory worker... This country's biggest competitor is probably Germany, and definitely not China.

Trade jobs. Welder, carpenter, plumber, etc.

Do you have reason to think the trades have enough aggregate demand to soak up the entire underemployed population at reasonable wages or is that wishful thinking?

Another question is if this underemployed population could see such great gains by moving to these fields why haven't they already? It may be that they aren't capable of doing these jobs.

Jobs that will pop into existence if we train people for them, I'm sure.

Only if they are willing to accept lower wages which is exactly what we are trying to avoid.