I'm being repetetive here, but I don't see this as a failure of senate rules. If anything, it is absence of hosue rules (and this came up hard in the "rules committee" hearing on impeachment, how biased the house process was).
The DEMs are violating axiomatic norms of conduct. Not the least of which is all the hoaxes, plus the bad faith construction of the July 25th call.
It's akin to blaming the rules for the conduct of criminals. Some people just don;t know how to behave in polite society, and it's a fools errand to try to get good behavior by passing more rules.
You are correct, the House is violating norms. And they are violating reason. As has been pointed out they called him a cancer, a grave threat to the country, to our allies, to the world. To use your word it is axiomatic - if you impeach the POTUS that means you think he has committed Bribery, Treason or other high Crimes and Misdemeanors and that he must be removed. So delaying the process makes absolutely no sense if you sincerely believe that. Why allow such a person to remain in office?
She is abusing the power of impeachment for political exploitation. Accordingly she must be held to account. She must pay a price. I think the Senate can make her pay one.