"Solid fast" is an old expression, it seems to survive in sea songs. It means to hold steady, without deviation, or that something is attached solidly, secure, rigidly, etc.
It is in Roget's Thesaurus. I'm curious about when it came into use and if it was originally nautical. Not important for any reason, but wondering how it was first used.

The shanty posted by Sinsull is known in several forms; as "Oh, My Rolling River" on Nevis. (See Roger D.
Abrahams, "Deep the Water, Shallow the Shore," pp. 73-74. In all of them, "misery" is used; it is sung in squally weather.
It is believed that the song was obtained from whaling ships, which afforded employment to West Indian sailors and fishermen.