This is how I read Brenner's logic:
Fraticidal competition->cost cutting technical change->overcapacity of high cost producers->lower average rate of profit->slower rate of accumulation->devaluation of high cost capacity (possibly delayed by real wage cuts, currency manipulations and debt)->higher rate of profit and accumulation on total social capital following upon devaluation.
This is how I read Marx's argument:
upward pressure on OCC->shortage of surplus value vis a vis accumulation requirements->reduced effective demand for growing commodity output->crisis of general overproduction and excess capacity->outbreak of fraticidal competition-> acceleration in the concentration and centralization of capital on a global scale along with growth of world reserve army of labor, boosting the rate of profit of the surviving capitalists.
So Brenner takes as given what must be explained: breakdown of Marx's capitalist fraternity or what Schumpeter called correspective competition and the outbreak of fraticidal competition. Competition is not always fraticidal even between national capitals on the world market. Competition is invoked to explain everything when fraticidal competition itself is what needs to be explained. Grossmann and Mattick are very clear about this.
In short, it is the shortage of surplus value, rooted in the very capital-labor dynamic which Brenner self-consciously wants to subordinate to intra- capitalist competition esp at the international level, which has explanatory primacy in Marx's crisis theory.
I don't think Brenner's theory is a continuation of Marx's project.
However, if the rate of exploitation is always growing sufficiently and great capital savings innovations are always available and new low OCC branches are being continuously introduced then the mass of surplus value may never fall short of the requirements for capital accumulation. It may simply be a question of the maldistribution of surplus value due to disproportionality or underconsumptionism. The competitive process can solve the former; reform the latter. And none of the unpleasantries of Marx's analysis need be faced.
best, rakesh