When Littlefinger learned that the Tyrells planned to marry Sansa to Willas, why did he go to the Lannisters rather than simple accelerating his own plans to extract her from Kings Landing?

Because Sansa wanted to go to Highgarden and wouldn’t have been willing to leave with Dontos. Moreover, if Sansa comes to him having been forcibly married to the Lannisters and a fugitive from royal justice, she’s way more dependent on him than she would be otherwise.