The sea level speed quoted in the question for the Pascal-A manhole cover is likely in error. It came from an informal conversation between Bill Ogle and Dr. Robert R. Brownlee about back-of-the-envelope calculations (done by Brownlee) concerning the upcoming Pascal-B test. Brownlee, himself, denies the speed is valid.
The US-manhole-beats-Sputnik-into-space-story is firmly entrenched in Cold War mythology. Questionable information has morphed into hard fact by frequent retelling. But calculating the trajectory of the manhole cover using erroneous estimates is like calculating Santa Clause’s trajectory from the North Pole: it provides quantitative validation to a mythical flying object.
Original sources (including the cine frame) are scant, but this conversation is reported by Brownlee in the Nuclear Weapons Archive,
“Ogle: "What time does the shock arrive at the top of the pipe?"
RRB: "Thirty one milliseconds."
Ogle: "And what happens?"
RRB: "The shock reflects back down the hole, but the pressures and temperatures are such that the welded cap is bound to come off the hole."
Ogle: "How fast does it go?"
RRB: "My calculations are irrelevant on this point. They are only valid in speaking of the shock reflection."
Ogle: "How fast did it go?"
RRB: "Those numbers are meaningless. I have only a vacuum above the cap. No air, no gravity, no real material strengths in the iron cap. Effectively the cap is just loose, traveling through meaningless space."
Ogle: And how fast is it going?"
This last question was more of a shout. Bill liked to have a direct answer to each one of his questions.
RRB: "Six times the escape velocity from the earth."
Bill was quite delighted with the answer, for he had never before heard a velocity given in terms of the escape velocity from the earth! There was much laughter, and the legend was now born, for Bill loved to report to anybody who cared to listen about Brownlee's units of velocity. He says the cap would escape the earth. (But of course we did not believe that would ever happen.)
The next obvious decision was made. We'll put a high-speed movie camera looking at the cap, and see if we can measure the departure velocity. In the event, the cap appeared above the hole in one frame only, so there was no direct velocity measurement. “
Dr. Brownlee was later quoted, "I have no idea what happened to the cap, but I always assumed it was probably vaporized.”
The fate of the manhole is dealt with in this excellent posting on our favorite website: https://physics.stackexchange.com/questions/488151/could-the-end-cap-of-the-pascal-b-1-survive-its-trip-through-the-atmosphere
Without a reliable launch velocity, the hypothetical orbit cannot be calculated.