I agree with your calculation.
On January 1, 2019 you will have stayed in Denmark 6 years (and maybe little more), and therefore meet the requirement in 2019.
In 2019 only 01.01.2007-01.05.2010 is counted from your "first" period in Denmark. Because we go 12 years back from January 1, 2019.
Also in 2020 you will have stayed here little over 6 years.
But in 2021 only 01.01.2009-01.05.2010 can be counted from your "first" period in Denmark. So after this you will still only have stayed here in little over 6 years also in 2021.
But in 2021 this will not be enough, because the requirement will be full phased in and be 7 out of the last 12 years.
So as I see it you will be able to get dagpenge in 2019 and 2020, but not in 2021, 2022 and 2023.
In 2023 nothing of your "first" period in Denmark will count, because it will then be more than 12 years since.
And yes, I also agree that from 2024 you will meet the requirement.
This case/situation is not mentioned in the new law, and therefore we can not say what the practice will be or how the A-kasse will process your case.
posted by a danish company? Only if you was posted by the danish subsidiary, and you kept your employment with the danish subsidiary during your stay i US, then you will be able to count this as stay in Denmark. Also it requires that you kept a connection to Denmark, while working in US.
The danish subsidiary must be registered in Denmark (CVR-register) and must perform activities in Denmark.
studying abroad? You did not move to US for studying, so you can not use that exception. I assume it was "normal" work in US, and not education.
Is Lønsikring affected by the new law? Whether the law is applied to TopDanmark Lønsikring, you must ask TopDanmark about. The extra salary insurance is a very different product than the normal Unemployment Insurance, and the different Insurance companies can have specific terms and conditions.
So you must ask TopDanmark.
We can only recommend you also to ask your A-kasse.