Saw this via another news source.
That story contained critiques similar to those you raise - just not enough punch to do any good in a layer multi-hundreds of meters deep.
In extremely rough outline, somewhat reminds me of the FIDO experiments in WW2 (Fog, Induced Dispersion Of, or some such title). That at least worked, using both heat and the lift of rising heated air - but was not economical (roughly, the fuel burn rate of five A380s running at once).
However, that does raise the points that HOT jet exhaust will:
1. add its own lifting power (hot-air-balloon-style) to the mechanical jet blast
2. will heat the cooler trapped air beneath the inversion, lessening the intensity of the inversion
and targeting the flow at the pollution source means one is not trying to lift the whole trapped air mass over the city, simply the pollutants where they exit the stacks.
Seems to me if the general principle can work at all, it makes more sense to put the "reheat" engines directly into the top of the smokestacks (with side inlets so the jets are not soley breathing the coal fire's own CO2 output and particulates). That also adds ~100 meters to the effective height.