It is possible the OED version online is abridged. I think I read something of the sort on the website, but unfortunately I can't access it any more via your link (though I could at first, strange...). If it is indeed the unabridged version, I dare say it will be difficult for you to find more extensive commentaries.
The fact that you found a PIE root mentioned under a certain entry in dictionary A but not B could of course mean that dictionary B erroneously omitted a widely accepted etymology for this word. But it could also mean, and I think this is the more likely explanation, that B's editors omitted it because they thought the evidence is not sufficient to include this etymology/reconstruction.
You also asked for literature that "connects or explains ... the evolution of meanings". I am afraid it might be difficult to find such literature for a wide range of words. Etymological dictionaries are concise in the information they offer because it is expected that readers will know common sound laws and other developments that will fill many of the "gaps" you mentioned. It's not as if every reader will go away with all questions answered, but most of them are. What is available in terms of more extensive literature on specific words will mostly be unsatisfactory because the discussions will be quite specialised.
My recommendation is, similar to jlawler's, that you read a good textbook, such as Baugh & Cable's The History of the English Language. In addition to this, or if your interest very narrowly focusses on sound change, you might want to read what Wikipedia has to say on sound laws. Verner's law and Grimm's law are particularly well known.
If you pursue any of this, it will lead you a bit away from looking at specific words and their reconstructed history. Instead, you'll get the larger picture of how languages develop and change. It's a bit like the difference between learning how many electrons there are in an iron atom, and what that actually means for the chemical reactions that iron can be involved in. I'm not saying that looking at specific words and their histories is wrong, but it can only get you so far, and it's possible you have exhausted this avenue.