I don't quite understand your statement, "I've got ANSI 31.3 barred tee fittings while the pipe is ANSI 31.8 and 31.4."
You need to determine which piping code has jurisdiction over your system, B31.3, B31.4 or B31.8, and calculate the required wall thicknesses of your pipe and fittings (tees & elbows) using the equations and allowable stress values from the appropriate code.
If you are using a higher strength Line Pipe with lower strength Fittings, then your fittings will require a thicker wall. If that's the case, you DO NOT WANT TO BEVEL OR TAPER BORE the fitting to match the pipe. If the fitting is weaker, you need to maintain full fitting thickness for all of the fitting. B31.4-2002, Fig. 434.8.6(a)-(2) detail (c) shows an example of a butt-weld that you would use that will maintain full strength in the weaker component.
NozzleTwister
Houston, Texas