This dialogue is not the most flexible of sorts. But what happens is, it shows an aggregate of your templates and their fields, with little way of controlling the order they appear in.
One thing you can do however, is organise the fields under different section names. You currently use
Content for all of them, meaning all the fields will end up in the same grouping.
By organising the fields differently, e.g. use
Links, as section names - this dialogue will organise the fields more to your liking I believe.
And yes, you can use the
__Sort order on the section items to control the order of how these sections appear in the dialogue as well.
Additional Reference: Field Ordering When Inheriting Sitecore Templates
Edited to add
I actually think you can sort all of the fields even if you remain in the same section name. But you would need to manipulate the
__SortOrder of the fields directly. So on the fields under one template, you set their sort order to
30 and so on. In the next template, to
300 etc. And so on. Generally Sitecore would respect the overall sort order - this is why it's "interleaving" the fields to begin with.
That said, I think it's easier to just group by different section names. That's one of the only reason sections exist, after all.