Sure, I can if it makes you happy, but I don't know what you mean by that "flaw". I watched those videos years ago. You would have to explain it in detail for me to address it, and/or give me a timestamp.
But the main issue is that you're not watching the videos and you're trying to make arguments to defend the model instead.
A couple of problems that I can see right away.
If you look in the first of his videos that you posted, around the 7 minute mark, you'll see that he is doing something of a 'pick and mix'. He is taking the distances from the ephemeris data on the horizons website, but is taking his tilt and elliptical parameters from the 'Earth facts' website. The problem with that is the earth facts data is, as per its factsheet, not particularly accurate. The orbital data, for example, when he looked at it, came from the year 2000, and was a mean value of a constantly changing parameter.
The next problem builds on that - he's taken each year, divided it by two, and created two perfect ellipses, based on the 2000 average figures for eccentricity and the ephemeris figures for the range from the sun, with a correction made in the second ellipse to bring the finish point into alignment with the distance from the sun of the following January. The problem is that the ellipse the earth is on changes constantly - doing it in the way he's done is a simplification. It's a small amount of error, but when you're trying to predict eclipses it will be enough to throw the result.
He is then triumphantly wondering why the moon and sun are not precisely where they were predicted to be according to the azimuth and elevation figures at, for example, the eclipse. If he'd have used one of the coordinate datasets - those are tick options on the menu of parameters on the horizons page - for the actual position of the earth and moon, with respect to the sun, instead of trying to build his ellipses the way he did, then I suspect he'd have achieved 'better' results, if indeed that's what he wanted to happen.
They may be other errors in there too. I'm not going to wade through 3 hours to find them.