Article One, Section Two, Clause Five...
"5: The House of Representatives shall choose their Speaker and other Officers; and shall have the sole Power of Impeachment.
Now, you must understand that there is a process which ends up being boiled down to an article of impeachment. This "process" includes whatever evidence gathering there is that is necessary to formulate the article of impeachment that will be presented to the Senate. "Sole" power to impeach does not give leeway to the Senate in any capacity to partake in evidence gathering as it relates to the process of impeachment. If there is new evidence, it is the responsibility of the House alone to discover it, and if need be, formulate a brand new article of impeachment. The Senate is forbidden from helping them do this.
We'll just have to agree to disagree.
In my view you're trying to limit the Senate's ability to try the impeachment, something that the Constitution doesn't do.
I will point out that none of the President's legal team are making the argument that you are, and they're throwing up lots of different theories.