The problem with that being that it was not shut down, and American Episcopalians had begun separating themselves from the Church of England before the Constitution was ratified. So as a precedent for how to deal with Islam it falls far short.
While many of the colonial population were patriots of American independence, most reputable historians estimate the number of loyalists (to Church and King) at 1/3 with another 1/3 neutral. At no time during the struggle were the founding fathers in the majority. As for specific numbers of clerical loyalists and what it took to effect the change from "Church of England" to Episcopal, here's a wikepedia excerpt [Link]:
"Of the approximately three hundred clergy in the Church of England in America between 1776 and 1783, over 80 percent in New England, New York, and New Jersey were loyalists. This is in contrast to the less than 23 percent loyalist clergy in the four southern colonies.[25] Many Church of England clergy remained loyalists as they took their two ordination oaths very seriously. Anglican clergy were obliged to swear allegiance to the king as well as to pray for the king, the royal family, and the British Parliament.[25] In general, loyalist clergy stayed by their oaths and prayed for the king or else suspended services.[25] By the end of 1776, some Anglican churches were closing.[25] Anglican priests held services in private homes or lay readers who were not bound by the oaths held morning and evening prayer.[25] During 1775 and 1776, the Continental Congress had issued decrees ordering churches to fast and pray on behalf of the patriots.[25] Starting July 4, 1776, Congress and several states passed laws making prayers for the king and British Parliament acts of treason.[25]"