The two verbs developed different from the Proto-Indo-European verb steh₂. Once they evolved into Proto-Germanic (ancestor of English, German, Dutch, etc), that verb split into two. In English we use the descendant of 'standaną', the Germans used the descendant of 'stāną'. Both of these mean the same thing and are supposed to have the same past tense. I am baffled as to how stand- (standest, standen etc) became the past tense in Modern German, since it was supposed to be forms like stōþ (stoth), *stōst which we do still have (stood) in some form! Source: https://en.wiktionary.org/wiki/Reconstruction:Proto-Germanic/st%C4%81n%C4%85 https://en.wiktionary.org/wiki/Reconstruction:Proto-Germanic/standan%C4%85
In fact "over there" is the closest translation to "da drüben" or "dort drüben", whereas "da" und "dort" are more like "there" alone. The difference between "da" and "dort" is only minimal, maybe "dort" is clearly referring to something distant, whereas "da" can be used for nearer and farther things (but not, if it is contrasted with "hier", in that case it is the reference to the more distant thing).
You may be right, but I would have thought that your suggestion would apply more clearly to the German perfect tense (which could translate to either "I have stood" or "I stood") but not exactly to the preterit, which we have here.
I think, nevertheless, that both the preterit and the perfect can mean "I was standing", "I did stand", etc.
Grammar sites are somewhat inconsistent, but the following sites say there's a difference between the perfect and the preterit, in that the perfect can denote a connection to the present (which would correspond more closely to the English present perfect tense):
The journalism example given on the second site is an interesting example of the difference.
(Please, if someone disagrees, explain, rather than downvoting. References would be appreciated.)