I mean you're correct that Presidents never write their own EOs. They require sophisticated legal knowledge to author. Leaving aside the fact that this EO is completely in line with Trump's obsession with overturning the results of the election at all costs, what you're positing isn't remotely plausible.
The very notion that a staffer would just elect to draft an official order to have the US Military seize control of voting machines in areas where Trump lost the vote without getting Trump's buy-in is beyond absurd. We're talking about a military intervention into an American election because the sitting President wants a different outcome
Doing that on your own volition would get you fired on the spot or even potentially worse. These things are a matter of record, and prior to 2020 apparently, that's exactly the kind of thing that destroys an administration and potentially lands people in Court. You would NEVER risk having that on the Administration's record unless you knew the President wanted it to happen.
I'll also point out that this was widely reported on months ago. Trump himself lobbied for this idea, among other equally disturbing options, to help overturn the election.
Gulliani even went to DHS to ask them to do it.
You actually think he would do something like that without authorization?
The fact that you're making excuses for this is concerning.