Some showrunners, eager for progress in the Hollywood strike, want the Writers Guild of America to meet with studios. How much sway they still have is in question.With the Hollywood writers’ strike stretching into its fifth month and the financial toll on people across the entertainment industry becoming increasingly grim, A-list showrunners have grown impatient.Some have called union leaders to ask pointed questions about the stalled talks. Why can’t you get in a negotiating room with studio representatives and not come out until you have a deal? Isn’t it time to bring in mediators? Others have pushed for a sit-down to hear their union’s strategy for resolving the strike. Union officials are scheduled to meet with Kenya Barris (“black-ish”), Noah Hawley (“Fargo”), Dan Fogelman (“This Is Us”) and other restless showrunners in the coming days. Whether marquee writers have enough juice to help end the dispute — as they did during the 2007-8 screenwriters’ strike — is an open question, however. The power dynamic has changed inside the union since then, longtime Hollywood observers say, and showrunners no longer hold the same sway.“You’ve seen a weakening of showrunner influence and a resurrection of rank-and-file writer influence,” said Stephen Galloway, the dean of Chapman University’s film school.The Writers Guild of America, which represents more than 11,000 television and film writers, and the Alliance of Motion Picture and Television Producers, which bargains for studios, have not held talks for three weeks. Last month, studios sweetened their offer — and then, in an unusual move, publicly disclosed the details, hoping rank-and-file guild members would be satisfied and pressure their leaders to make a deal.“This was the companies’ plan from the beginning — not to bargain, but to jam us,” guild leaders said shortly afterward. “It is their only strategy — to bet that we will turn on each other.”Union leaders have since insisted that the onus is on studios to keep improving their offer. The studios have rejected that demand, but it is a position supported by many Writers Guild members, including numerous showrunners. On Tuesday in Los Angeles, writers like Alexi Hawley (“The Rookie”) and Scott Gimple (“The Walking Dead”) helped stage a well-attended “showrunner solidarity day” picket at Fox Studios.“I don’t think anybody is really second-guessing and looking for ways to cause some disruption in the leadership of the guild,” Steve Levitan, whose credits include “Just Shoot Me!” and “Modern Family,” told a reporter for an entertainment trade publication at the event. “We’re just always trying to see if there are any ways anybody can help.”Behind the scenes, however, frustration among elite Writers Guild members has been mounting.Ryan Murphy, the writer-producer behind television hits like “American Horror Story” and “9-1-1,” recently had a heated conversation about the strike with Chris Keyser, a senior Writers Guild official, according to two people close to Mr. Murphy, speaking on the condition of anonymity to describe a private discussion. Mr. Murphy set up a financial assistance fund for idled workers on his shows and committed $500,000 as a starting amount. Within days, he had $10 million in requests, the people said.Tyler Perry was among the show creators planning to meet with guild leaders.A spokesman for the Writers Guild declined to comment.At 135 days, the strike is one of the longest in the history of the Writers Guild. (The longest was 153 days in 1988.) The union has called this moment “existential,” arguing that the streaming era has deteriorated its members’ working conditions and compensation levels. Studios have defended their proposal as offering the highest wage increase to writers in more than three decades, while also offering “landmark protections” against artificial intelligence.Studios have also signaled a willingness to negotiate with the guild on the sticky matter of staffing minimums in television writers’ rooms. (The studio alliance declined to comment for this article.)In July, tens of thousands of actors represented by SAG-AFTRA joined writers on picket lines, the first time both unions have been on strike at the same time since the 1960s.The result has been a near-complete shutdown in Hollywood production. Writers and actors have lost income, of course. But the collateral damage is also mounting, with crew members and support staff beginning to feel a severe financial squeeze. Hollywood workers have taken $45 million in hardship withdrawals from the Motion Picture Industry Pension Plan since Sept. 1, according to a document compiled by plan administrators that was viewed by The New York Times. Workers have been allowed to pull $20,000 each from their retirement funds for the time being.Showrunners like Mr. Murphy and Mr. Fogelman employ thousands of crew members across their productions, putting them in the position of being besieged by people who ask when they can get back to work and having no answers.Conventional wisdom in Hollywood held that the strikes would be resolved by Labor Day. Now time is running out to salvage the year, given the time it takes to reassemble casts and crews, a complex process complicated by the coming holidays. Preproduction (before cameras roll) for new shows can take up to 12 weeks, with movies taking roughly 16 weeks. Even if the Writers Guild and studios can come to an agreement in the coming weeks, studios need to engage with the actors’ union, and no talks in that dispute have been scheduled, either.Showrunners have gotten more involved as studios have suspended first-look deals worth millions of dollars. Last week, Warner Bros. suspended deals with J.J. Abrams, Mindy Kaling, Greg Berlanti and Bill Lawrence.Yet despite the real implications that this strike is having on all ranks of the business, no guild member wants to be seen as agitating against the union’s leadership. Prominent showrunners are concerned about having their names in public and are instead trying to push things forward without looking like elites who aren’t in alignment with guild leaders. The appearance of dissension in the ranks scuttled a meeting this week between showrunners and Writers Guild officials, with both groups subsequently bickering over who canceled on whom.As the 100-day writers’ strike in 2007 wore on, a group of showrunners pushed union leadership to settle with the studios. But several entertainment executives said showrunners were more of a power center within the Writers Guild 15 years ago. For one thing, there were just a few dozen of them.In recent years, as the showrunner pool has expanded to hundreds, some Hollywood observers have argued that their influence within the union has waned. The limits of their power were on display four years ago in a failed attempt to wield influence to end another Hollywood stalemate.In 2019, Writers Guild leaders told thousands of screenwriters to fire their talent agents over what they described as significant conflicts of interest. As months passed, with the agency standoff showing no signs of resolution, some marquee writers went public with objections over the union’s strategy. They said the dispute with the agencies was a worthy one, but they objected to a seeming lack of urgency in returning to negotiating.One of the opposing writers, Phyllis Nagy, who was nominated for an Oscar in 2016 for her “Carol” screenplay, ran for president of the Writers Guild’s West Coast branch. She was vying to unseat David Goodman (“Family Guy”), who was standing for re-election. A who’s who of showrunners and writers — including Mr. Murphy, Mr. Berlanti, Shonda Rhimes and Ava DuVernay — endorsed Ms. Nagy.But Mr. Goodman won re-election with a strong majority. He is currently a chair of the Writers Guild’s committee squaring off against studios for a new contract.In the fight with agencies, the Writers Guild held firm for nearly two years. Many people in Hollywood have credited that lengthy dispute — ostensibly won by the Writers Guild — as galvanizing union leaders in the current standoff with studios. More