The solution as to where to bury the remains of Richard III is a rather simple one.
Not Leicester. Not York. But Fotheringhay.
The Church of St Mary and All Saints, Fotheringhay, Northamptonshire is the site where Richard III himself once oversaw a rather significant reinterment -- the reburial of his father, Richard, Duke of York.
Richard III's mother, Cecily of York, was also later buried in Fotheringhay.
St Mary and All Saints's is a humble enough attraction to accommodate for Richard's infamy, yet grand enough to house the body of a York nobleman.
Perhaps Elizabeth II can put forth this Solomonesque peace offering to the now-warring cities of Leicester and York.