Seeking Ships Records USS Connecticut BB-18 (1921-1923)

My grandfather was on the USS Connecticut after WW1 during the years of 1921-1923. He supposedly used a fake name and DOB to get into the Navy so I cannot find any service records for him. I have written to the St. Louis National archives but they were unable to locate any records for the possible names I gave them. I have a photo of a Co. J.M.M.G. Math Class Great Lakes, Ill Dec 4, 1???.that he is supposed to be in. The year is whited out but it is probably either 1921 or 1922 or could even be 1920. I have another photo of a post card that was sent to him on the USS Connecticut by his friend dated Feb 28 1923. The post card was addressed to L.Tadra, CONN.

Birth Name: Lucyan Tadrzak

DOB: 04 Feb 1904

POB: Kapusnik, Poland

May have lived in Allegheny County Pennsylvania during that time period

Other Names: Lewis Tadrzynski, Lewis Tadrzinki or Lewis John Tadra (legally changed to this in the 1940's)

Fathers name: Stanislaw Tadrzak

Seeking:

1. Ships rosters, musters and pay information for the USS Connecticut BB-18 from 1921-1923

2. Great Lakes Class rosters for the time period 1921-1923

If these are not online where would I need to go tot research them? I am willing to travel to St. Louis or DC.

Thank you,

Jeff Cooper