The solution is for governments to do the investment directly and at current interest rates. It can either tax those who are holding the savings glut or just ignore that money and create new money, well, at least those sovereign in their own currency can.

and this:

We would get a twofer: put the economy back on track to full employment and do everything we can to save the planet.

and this:

But they have assets and expertise that likely could be redeployed profitably as well.

On this:

But my point is that we cannot expect the private sector to so use the savings glut.

Can't we influence them to start investing their savings glut productively by (1) penalizing savings over a certain amount and/or a certain amount of time; (2) taxing certain types of consumption and investment (e.g. on fossil fuels and their derivatives), and (3) providing incentives to invest on socially and environmentally "positive" investments, e.g. renewable energy?

Though on that last point, there is this allegation:

Like Mao urging peasants to melt down their pots, pans and farm tools to turn China into a steel-producing superpower overnight, Germany dished out subsidies to encourage homeowners and farmers to install solar panels and windmills and sell energy back to the power company at inflated prices. Success--Germany now gets 25% of its power from renewables--has turned out to be a disaster.

As Germans rush to grab this easy money, carbon dioxide output has risen, not fallen, because money-strapped utilities have switched to burning cheap American coal to provide the necessary standby power when wind and sun fail. ...

Germany Reinvents the Energy Crisis - A love affair with renewables brings high prices, potential blackouts and worries about 'deindustrialization.'
Holman W. Jenkins, Jr., Wall Street Journal