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Hi Beth -- thank you for posting to History Hub!
I'm not sure which version of this address is the "official written version." The U.S. House of Representatives version you point to has: "do not print this as pub[lic] document" written across the corner, so I'm inclined to view it as a draft.
The House did publish a version of the address as H.Doc.174, 87th Congress.
H.Doc.174 appears, at a glance at least, to be what's published in the Congressional Record. The Congressional Record is the official record of proceedings and debates of Congress. It's published daily when Congress is in session and is available online through the GPO and Congress.gov.
I would view the speech as it appears in the Congressional Record as the closest to what was actually spoken by President Kennedy before Congress.
The version that appears on the American Presidency Project is a digitization of what's in the published volume: Public Papers of the Presidents. These volumes are compiled by the Office of the Federal Register beginning in 1957. Each volume contains the papers and speeches of the President that were issued by the Office of the Press Secretary during the specified time period.
I would recommend contacting the John F. Kennedy Presidential Library and Museum for further insight. They will hold more versions of the President's speeches and may be better equipped to identify an "official version." In fact, the JFK Library has posted a video excerpt of some of the address in question with a transcript.