I looked for different H limit taps in 5/16-32 from McMaster-Carr, and they only have H3, which is standard fit. Not sure what that means exactly, but H5 is very loose fit, and H2 is tighter tolerance than H3.
The threads in the barrel will be weaker than the liner, since the barrel steel doesn't have as high tensile strength as the liner. You definitely want a good fit, liner to barrel.
Blah, blah, blah.
Tom