With regard to their record keeping, do you mean when it includes tests that you didn't do? If that's what you are referring to, on your results page there is a thing to change on the bottom left of the results field. Something regarding only displaying the tests from YOUR connection ID. Change that, and you will only see your tests from now on.
As for what the reps will need, right now only your Hughesnet performed tests will be accepted, but at least you've done them there, so they will be able to look at the results. The reason for this is that in order for the reps to accept the testmy.net tests as valid, they need to be done with the manual 12MB size for download tests and the manual 2MB size for upload tests. But, you stated that you've been doing tests at Hughesnet, so they'll have a record of those.
You started this thread two days ago. So, in the two days since you started this thread, without any input from the Official Reps, who aren't on here on the weekends, nor on holidays, nor the engineers, you've automatically come to the conclusion that "there is nothing that can be done about it."
Or, again, and perhaps I just missed it, where is a prior thread in which you brought up a speed issue, the Reps and engineers addressed the issue, and the ultimate conclusion was that "there is nothing that can be done about it?" I've yet to find anything to justify that conclusion, but I'd be happy to read it if you could post the thread.
The second set of test will most certainly help more than the first. But, with that said, they may ask you to run a few tests (not that many) at various times of the day to get an idea of patterns and such.
With that said, if you do the automated tests again, at the various times of the day (and I didn't realize you could set the speed, time space, and number of tests, so that's a great find for me), I would use the same size that you did in the second tests, set them to run five minutes apart, like you did, but set it to only run five tests. What you did is great, but it's really overkill, and you don't want to waste precious data. No one wants to use more data than they have to. A block of five tests, each set five minutes apart, and a block at various times of the day, preferably one in the morning, afternoon and evening, if you can, is really what would be the most helpful.
Again, hopefully there is something they can do. There may very well be.