Your explanation was fine.
I doubt the IRS made a mistake. And if they did, they're not going to find it of their own initiative, because they consider your amended return to be a completed item. And if they did, I doubt you sending in a second amended return is going to trigger them realizing it.
I'd cash the check and send in the second amended return now. The IRS is certainly able to keep much more complicated things straight, so I don't think you're doing anyone any favors by waiting on either of these items.
Their notices and letters are generic, so they pick the one that is closest to applicable. In your case, since you have qualified dividends and are using tax software, your tax calculation is probably done on the qualified dividends and capital gains worksheet, of which there is some version in the Schedule D instructions. So that may be the connection.
As for why they apparently gave you too much, you should be getting a mailed notice, which will have verbiage about what to do if you disagree with what they did. You can respond to that if you want, or just accept the $800 - again, the chances that you're right and they are wrong is very very low.
One other thing you could do is go get an IRS account, log in, and request transcripts for tax year 2019. Going through those line by line with your second amended return may eventually help you debug and identify the reason for the difference. Then you'll have some understanding to go on.
The only thing I can think of generally is that your change in qualified dividends had some sort of cascading effect that your software didn't account for but the IRS computers did. I can't imagine what that might be regarding qualified dividends, but an example of the sort of thing I'm thinking about is a reduction in AGI could move you under a breakpoint for the retirement savers credit - moving you from 10% to 20% or 20% to 50%. But your tax software should have probably included that, unless you somehow made a mistake during the amending process. Although, given that you're still amending your 2019 return and are on your second amendment, that seems like a reasonable possibility to me.