The NOS 7027A is about the same as a 6L6GC in your B-15N. Depending on the make, the two types are either identical or the 7027 is built a bit better. There are some 7027's that are taller and may not fit under the tube cage so check that out.
If your tech is modifying your amp in a way that raises the B+, that would be a reason to go with the 7027. If you are pushing your amp, you might want to try a solid-state rectifier module in place of the 5AR4 tube and see how you like it. It might give you the clarity that you are looking for.
Bottom line, if you like the result with the 7027 installed, go for it. He can install the 7027's and you can try it, then try a set of 6L6GC's and see. In terms of wiring for each tube type, you never know what was done to the amp. Someone might have wired the amp to use the unused pins on the tube socket. So despite what the schematic says, check the amp wiring to be sure.
Did he tell you why he feels that the 7027 is the way to go in your amp?