It has different locations for pre- and post-1953 discharge date.
The archives.gov website makes it sound as if it could be quite awhile before we get a response.
But more in-depth reading implies that the veterans who take a really long time to process are those whose records were destroyed on the 6th floor of the big 1973 fire at the St Louis archives, because whatever info is still available must be painstakingly "reconstructed from other records".
And it says that it was basically only Army & Air Force records that were destroyed on that floor. So his Navy records should have survived the fire.
OTOH, he was discharged 72 years ago, but it says that "Records are accessioned into the National Archives, and become archival, 62 years after the service member's separation from the military." And I don't know what the implications of that are ("accessioned"??? "Today's English class assignment: write a sentence using the word 'accessioned'") Does it mean a longer wait time or what?
Think I'll also try some of the other links and pointers to local organizations / govt offices that some of you posted. Thanks again!