If the Founders wanted the establishment clause to forbid endorsements as well as establishments then wouldn’t they have wrote it that way?
On motion to amend article third, and to strike out these words: 'religion, or prohibiting the free exercise thereof,' and insert 'one religious sect or society in preference to others:'
On motion to amend the third article, to read thus: 'Congress shall make no law establishing any particular denomination of religion in preference to another, or prohibiting the free exercise thereof, nor shall the rights of conscience be infringed:'Both were passed in the negative (rejected). It continues...
On motion to amend article the third, to read as follows: "Congress shall make no law establishing articles of faith or a mode of worship, or prohibiting the free exercise of religion, or abridging the freedom of speech, or the press, or the right of the people peaceably to assemble, and petition to the government for the redress of grievances:This was passed in the affirmative (later to be amended).