Well, according to Al-Mawrid,
صَمَدٌ = eternal, perpetual, sempeternal, everlasting
The root verb is صَمَدَ = he withstood, endured, lasted
For this reason, I would translate it 'Allah the Eternal'
i.e. Eternal in that Allah is beyond the realm of time; he is dependent on neither man nor woman nor jinn nor angel to supplement his existence; that he has lasted through every age and will continue to do so. In that sense, I can see your description of 'Independent' fitting in very well, as the next verse goes on to talk about the fact that he is neither begotten neither does he beget. He is the Creator of Us (Mankind) - and in order to engender that title, he must have to have 'been','be' and 'will be' - in other words, he must be Ever-lasting.
Does that make sense...?