Are you posting this because you actually believe it?
Ben Barnes? Is that even a real name? I grew up in Texas in the late seventies and early eighties and I never heard of that "prominent Texas politician." Results of a google search on "Ben Barnes" are nearly all "Benjamin Barnes," an obscure Brit actor. I saw only two about the "prominent" guy, the NYT story and the Daily Beast' regurgitation of it.
If the hostages had been released right before the election, that would not have reduced Reagan's incredible landslide in the slightest. If anything, people would have seen it as an attempt by the Ayahollah to sway the election and would have galvanized Reagan's support.
I hate to be that old dude that remembers history, but no one who sat in Jimmy Carter's gasoline lines during Carter's unemployment/inflation spiral thinks he could have won if only he had gotten the hostages released.
Read "Crises" by Carter's Chief of Staff, Hamilton Jordan. It is a shocking account of the hostage taking event and Carter's reaction to it. Shocking because it decribes U.S. officials begging Iranian mid-level government functionaries. Not begging for them to release the hostages, those Iranians had no authority whatsoever to do anything with the hostages. They were begging to be allowed to talk to someone who did. For more than a year.
On Reagan's inaguaration day, the Carter negotiators started packing their stuff. The Iranians asked when the Reagan negotiators would get there. Carter's men said there aren't going to be any Reagan negotiators, he promised that during the election. This was not a tell-all book by a staffer who turned on his old boss. Jordan was proud of working for Carter.
No matter. The Iranians decided they had fucked around, but din't want to find out. The hostages were released pronto, Reagan fixed the economy, and drove the Soviet Union out of existence without firing a shot. That last was his real crime to old-school Democrats, who will never forgive him.