How would Chess have been played in England in 1450-1600? I'm trying to reconstruct how Chess would have been played at various points in history in England, specifically at three points: around 1450, 1530, and 1610.

What rules would have been used at these dates? What kinds of boards and pieces might have been used? Who would have played and in what kinds of settings?

I have read the confused Wikipedia articles and most of the first several pages of hits from Google, but can extract little of use from them and am hoping there's an expert here who can help.
I see that you already have a lot of information in the Wikipedia page and in the answer you got to the similar question in the history forum. Maybe your problem is that this is too much information for you, so I hope to be helpful in telling you just one thing, which is the most important thing.

There is a turning point in the European history of chess. This is something that happened sometime between 1475 and 1500 (the exact year is not known) in the south of Europe (probably in Spain, but there is no consensus). This event is a change in the rules of movement of the Queen and the Bishop. 

Until 1475 people everywhere in Europe played a version of chess (let's call it Middle-Age Chess) where the Queen (then called fers or visir) could move only one step diagonally, and the Bishop (then called Elephant) could move two steps diagonally. The other pieces moved as today (except for little details such as castling rules). This game was very slow because the two armies needed many moves to make contact, since the only long range piece was the Rook. 

Starting from 1500 people everywhere in Europe started to play a new version of the game where the Queen and the Bishop have their modern movement (let's call this game Modern Chess, because, except for some little detail, it was basically the same game we play today). This new game was much faster, and, for this reason more fun and incredibly successful. The new rules quickly spread everywhere in Europe, and the old game was soon forgotten. 

The change happened sometime between 1475 and 1500, more or less the same time when many other important events gave Europe its modern form (invention of the press, the discovery of America, unification of Spain, and more).

From this you can see that in 1450, in England people played Middle-Age Chess, while in 1530 they played Modern Chess, a very different game. In 1530, Modern Chess was a novelty, instead in 1610 the game was very well established, and by this time, many "scientific" books of analysis of the game and its strategy were already written.