When I ran for Congress in Texas in 1974 I learned something important from my press agent: that one of the most important ways to influence voters were local, mostly weekly, newspapers, but that they would not provide free coverage unless the candidate buys advertising, and the amount of free coverage will be approximately proportional to the amount of advertising purchased. I later learned the same rule applied to radio. (That was before talk radio had become as great a factor.) I also found that, despite their protestations to the contrary, the attitude toward the candidates conveyed in free coverage was strongly influenced by the amount of advertising bought either by the candidate or by his known supporters, especially local businesses. Thus, if you had the support of local car dealers, you were likely to get more favorable coverage because car dealers pay for a lot of ads.
Not all of the media depend for their revenue entirely on advertising. Some get a substantial part of it from subscriptions or street sales. Those respond to what they perceive (correctly or not) as what their readers are willing to pay for. Some of them have come to realize that this will depend on the season (more interest in election information in the weeks preceding an election) or on recent events (e.g., legislation proposed or enacted that adversely affects people in the market for the media outlet).
The main reason why electoral processes worked better to avoid rent-seeking behavior in the early period of the United States was that voters demanded political information and were willing to pay for it. If a newspaper published the entire text of long speeches by candidates, they would sell more copies, and sell more copies than their competitors who didn't do that, enough to offset the additional cost of printing more column inches.
So the key to solving this part of the problem is to find ways to get more voters to seek out and pay for political information, and to do so in the mainstream media rather than in magazines, newsletters, and the Internet.
Part of the problem is that too many voters don't really think there is enough difference among candidates in what they are likely to do to justify them making the investment in time and money in acquiring more information. This is the problem of "rational ignorance".
I once joked to friends that the way to solve the problem would be to require that in every election there be a candidate who, if elected, would enact legislation that would select a date at random from the calendar, then summarily deprive everyone born on that date of all his property and his right to acquire more, then throw him in prison for life, and to hide a clue in his writings and speeches that he is the one who would do that. It would only take a 1 on 365 chance of being reduced to poverty and imprisoned to motivate intense investigation of all the candidates by every voter. But in fact that is exactly what existing candidates promise all the time, albeit not in those terms. It is just that voters don't think it will happen to them. If they realized it could, that would make a difference.