Now that advertising drugs to the public had ballooned marketing budgets beyond R&D is that still true?

I imagine that dollar-for-dollar a non-profit with the right incentives and oversight could out do the VC-backed leeches driving up prescription med prices.

The US subsidizes drug development, that's about all. Other medical R&D doesn't really come out of any publicly funded research system, it comes from medical practitioners. The cost of US drug development subsidy is maybe $40 billion, accounting for basic research and development by pharmaceutical companies. This is pretty much peanuts compared to global healthcare spending. Also, this money is arguably not really that well spent, since most of drug development is useless, and nations can improve their health systems and outcomes much more through things like routine care and monitoring than they will through expensive research.

Can't we keep paying for the R and D and just not let a minority of private actors profit?

The vast majority of pure research has funding generated directly from government funds. Medical funding is roughly half from public funds. This wouldn't change with price controls. More profits don't lead to more research.