The solutions are suggested in the problems. Don't let the union control the entire profession. The AMA's (legislated, btw) stranglehold on the medical profession is limiting entry into the field, which in turn creates a scarcity of medical professionals, which in turn increases the rates they can charge. Open the market, and that problem goes away.
This sounds like a regulatory mechanism. Who should enforce it? The government? In that sense I agree - someone needs to watch the market and (re-)establish balances. But to come back to the topic raised by the OP. What do you do if a majority of your labour force thinks that the wage is too low?
How, exactly, does removing the legislated restrictions on a profession, and thus having a completely free market in that profession sound like a regulatory mechanism?
If the majority of the labor force thinks the wage is too low, then they'll be asking for higher wages, won't they? And "a majority" is certainly enough to unionize. But the minority that is willing to work for less is important, too. If the union tries to push wages too high, they'll pull it back down by working when the union members strike. So the union members had best be willing to work for wages that the company owners will accept, or when they strike, they'll be replaced.
Labor is a market product, too. And that means it's governed by the laws of supply and demand, just like any market product.