I think you are making stuff up.
A point of order is raised when a House rule has been violated. Are you suggesting that the Speaker can validate a bill whenever she wants, unless a member successfully accuses her of breaking the rules? That only works if not validating a bill is against the rules. Which means she can’t validate a bill whenever she wants.
Also, a point of order can only be raised when a bill, amendment, or motion is first read. It is meant to prevent any consideration or debate of that specific bill, amendment, or motion. You cannot raise a point of order after a vote has occurred, it’s too late. You certainly can’t use it for some random complaint, like “Why has Madame Speaker still not validated the vote from yesterday?”
Eventually, the House has to vote on a final resolution that says: “Resolved, Trump is impeached”. They can vote on whatever they want before that. They can select managers beforehand, change the language of the articles that will be in the final vote, or whatever. They can try to use procedural moves to engineer a specific outcome, for example the resolution may not be allowed to reach the floor unless certain managers are approved beforehand.
But once the resolution reaches the floor and passes, Trump is impeached. And that’s what already happened. It’s obviously too late to set new conditions.
“The Senate makes the rules” is not the only alternative to “The Speaker makes the rules”.
For instance, there could be a House committee that makes rules. They could delve into tedious detail about all the things that must happen to a bill, amendment, motion, or resolution. From beginning to end. They could call themselves the House Rules Committee.
And the HRC already made rules regarding the impeachment resolution, which specify all the steps that must occur for the House to pass articles of impeachment. They don’t mention anything about the Speaker getting involved after the vote.