Could you provide an example of what you're asking about as far as "political musings and settings"? I'm a little unclear on the question. It's important to remember that Shakespeare's goal was never an exact retelling of historical events. He took many liberties and totally fabricated large parts of his stories in order to provide quality entertainment (and to some degree reflect well upon the ancestors of the Queen).

with an arguable long tail tracing back to boilingbrooke's usurpation

As for the background, the Wars of the Roses' origin goes all the way back to Edward III who inarguably created the conditions necessary for the factions during the Wars to take shape. By all means Edward III was a great king, he did exactly what was expected of a medieval king...he had a bunch of children (including sons), and set them each up with great titles and estates to spread his influence throughout England.

It is a failing of Parliament and Edward III (and really his predecessors as well) that ultimately led to the chaos of the Wars. England never accepted a specific formula for succession, relying on the customs associated with primogeniture, but never codifying them into law. The next king was usually decided how we would expect, the firstborn male inherriting all titles and styles from his father. Edward, having had five sons, was considered secure....his descendents would be expected to undoubtedly rule England indefinitely.

Of course, we know how that turned out. After the Black Prince died and his son Richard II was crowned, then forced to abdicate, then probably killed, without issue, the waters around the succession became murky. Of course, by this point Bollingbrooke was already ruling as Henry IV, by emphasizing his male line descent. Lionel, Duke of Clarence was Edward's second son but he'd already died in 1368, leaving one daughter Phillippa, from whom the Yorkist claim would ultimately arise. As you pointed out, Henry Bollingbrooke (the son of John of Gaunt, third son of Edward III) usurped Philippa's grandson Edmund Mortimer, 5th Earl of March to become Henry IV by arguing that male line primogenoture took ptecident over the claim of Edmund through his grandmother.

Ultimately, the long unrest of the Wars led to a weakening of the nobility (many nobles having died, many titles having gone extinct, many large estates having been confiscated and changing hands). The Wars contributed to the degredation of the fuedal power system of the middle ages, and consolidated power in the monarchy, which is exactly what we saw in the end from the Tudor dynasty and it's very strong monarchs.

Another lasting change was the almost total elimination of the feudal baron armies that fueled the Wars. Once barons were prohibited from raising large armies without the consent of the King things mostly settled down. Henry VII made this change. The power and authority of the barons was diminished as they could no longer conduct their affairs by raising large armies and fighting one another (or the King), and rather began to settle disputes through the crown at court.

The stories the come from the Wars paint a picture of a complex and divided England but on the whole most of England was largely unaffected by the Wars. Both factions stood to take enormous losses by ransacking the countryside or pillaging towns so mostly the Wars were fought between large standing armies (pitched battle) and avoided destruction of each other's castles and fortifications (some long seiges took place, but usually far from populated areas).

Perhaps the greatest lasting effect of the Wars was the death totals. 24 noble lines went extinct during the period of the Wars and tens of thousands of foot soldiers died. This, coupled with mass casualties from the Black death and other diseases that ravaged medieval England (mostly prior to the Wars), meant that food was in surplus, as was available land and tennentcies, leading to increased trade with Europe. This is broadly viewed as helping to usher in a new era of prosperity that eventually became the Renaissance.