If Richard is to get a religious funeral, it would be fitting that he receive a Catholic one.
Cranmer was a correspondant with Calvin, and I suspect their theologies were not that far apart. Calvin was rather indifferent to forms of church government or shapes of liturgy. He was willing to let Polish reformers keep their bishops, and his own order of service was a kind of stripped down mass. He even suggested a weekly Eucharist but went along with his Geneva friends. In many respects Calvin was not a Calvinist.