She's got the ball. If she wants to move it forward, she has to take it to the Senate. It's her ball. Nobody is restraining her, nobody is telling her she lacks the power to impeach (that's done), nobody is asking her to wait.
She does not have the power to set Senate trial rules. She can complain, sure. She can demand, sure, but nobody outside of the House demanded the House change its rules on this impeachment. She has the sole power, she used it, and her part is done. She can deliver it to the Senate, or not.
Mitch has apprised the world what he thinks of the articles. Her ultimate options are still the same. She can deliver the articles or not. That's entirely her choice.
So yes, I suppose I agree with you. She is running her show, and she can do what she wants with the Articles. But she cannot direct the senate trial.
She certainly seems to be directing when they start the trial. They don't need her to walk over papers. The House's part in this is done. Why would he even react to her 'delay'? He should just move forward and be done with it.
She made a colossal blunder in making public demands on the Senate. Few things piss off a career politician more than having another politician outside their legislative body tell them how to do their job. And that sentiment is magnified about a thousand times for U.S. senators.