What exactly is the offset? Is there some threshold voltage the BJT requires before it starts conducting, maybe one should expect a ~0.7 V difference between the op-amp output and the load voltage? There should be some opamp configuration where can you can bias the feed back to the -ve pin of the op-amp: this is commonly done for op amps running with single sided supply.
Is it possible to make use fo the full +/- 15 V range?
Also, want to use a FET on the output BJT, it has lower noise and better thermal stability.
So I put together a little test circuit to test out a NPN BJT buffer circuit with a TIP122 transistor and an OP27 op amp. Power voltages are ~ +-14V, just used the positive rail as V+ for the transistor.