You're still seeing it like an Anglospheric observer. For you, stagflation is caused only by supply-side problems. Nominal rigidity is out of the picture because there is high inflation. The left-wing solution to supply side problems is real investment; not to increase the demand side (so raising taxes to fund these is fine), but to reduce unemployment by lowering production costs. You don't need to distinguish very hard between kinds of production costs, the market will sort it out, just decrease something. Maybe you buy national broadband grids, or national rail infrastructure, or whatever. Inflation is, as we know, everywhere a monetary phenomenon, so what you spend on doesn't increase inflation either, provided that you aren't printing money to fund it. So it is an issue for your central bank to worry about later, when unemployment is lower.
But the Latin American sphere is still dominated by old Keynesians. For them, they distinguished between voluntary and involuntary unemployment (your own Anglospheric model only has something quite similar to voluntary unemployment). Involuntary unemployment is set by the level of effective demand. But inflation is very high, and you can see shortages in the shops, so by definition this cannot be an effective demand shortfall. So the problem must be voluntary unemployment. Old Keynesian theory sets the level of voluntary unemployment in the way the neoclassicals of the 1920s (not the 1970s New Classicals - I didn't choose this terminology) did - it is determined by the rate of profit.
And if you contribute to the capital stock, then you reduce the rate of profit. If you fix a house, then the owners of existing houses find their rent going down. So investment only makes the unemployment worse. The price of capital must rise relative to the price of consumption goods, and you are doing exactly the opposite.
The Marx-flavoured old Keynesians would fold their hands and say: this is the crisis of capitalism, let the crisis continue until capital stock depreciates enough that the rate of profit is restored. The right-wing old Keynesians would say: this is due to an excessively high real wage, let it diminish until full employment is restored*. The left-wing old Keynesians would say: we must lower the price of consumption goods, by shifting the use of the existing capital stock from the production of capital to the production of consumption goods. Maybe you commandeer factories or something. In none of these do you simply invest more as a solution.
* the Anglospheric "new classicals" don't worry about general equilibration between markets, so in their own voluntary unemployment, there's no crisis of capitalism and there's no imbalance between capital and consumption good production. It's always excessively high costs. But this flexibility also means that left-wing new classicals can lower wage costs by lowering capital costs, letting the market do the wage/capital substitution for them; it's excessively high production costs, not just real wages in particular.