So what i do is try and find books which are written for the "educated common reader" by an expert who guides you through the original paper/book. It is still difficult to understand if you do not have the necessary background but at least you have a good starting point.
Some books in my collection;
1) Newton's Principia for the Common Reader by S.Chandrasekhar
2) Maxwell on the Electromagnetic Field: A Guided Study (Masterworks of Discovery) by Thomas Simpson
3) Einstein's Miraculous Year by John Stachel.
4) The Annotated Turing by Charles Petzold.
What we need is for a group of professors to get together and start writing a series on explaining the original papers to the "educated common reader" i.e. not too trivial nor too overwhelming. I think there is a huge market for this since it humanizes how science is done in real life which is fundamental for motivation.
'According to his sister's memoir, Einstein was anxious about whether his relativity paper would be accepted by the Annalen der Physik. After it was accepted, he eagerly anticipated an immediate reaction to its publication, even though he expected it to be critical. He was greatly disappointed when his paper was not even mentioned in the following issues of the Annalen. Sometime afterward, she recounts, he received a letter from Planck, requesting explanations of a few obscure points in the work. "After the long period of waiting, this was the first sign that his paper was being read at all. The happiness of the young scholar was all the greater, since acknowledgement of his accomplishment came from one of the greatest contemporary physicists. ... At that time Planck's interest signified infinitely much for the morale of the young physicist."'
From Einstein's Miraculous Year by John Stachel (Ed), 1998, P115.