Wait between UART frames
It's not strange at all.  Serial doesn't block while it sends.  When you call write that pushes the byte into the send buffer and that's all.  Then the code moves on to the next instruction, the delay(950) and during that time the serial data is actually being sent.  It takes about 1 millisecond for that to happen.
This solution works as long as the send buffer doesn't have anything else in it that's slowing you down and as long as you don't change the baud rate.  If either of those things happen then you need to recalculate that time.
A better solution would be:
  Serial1.write(sw_binary_train_1);
  Serial1.flush();
  delayMicroseconds(950);
  Serial1.write(sw_binary_train_2);
  Serial1.flush();
  delayMicroseconds(950);
  Serial1.write(sw_binary_train_3);
  Serial1.flush();
  delayMicroseconds(950);
  Serial1.write(sw_binary_train_4);
  Serial1.flush();
  delayMicroseconds(950);
  Serial1.write(sw_binary_train_5);
  Serial1.flush();
  delayMicroseconds(950);
  Serial1.write(sw_binary_train_6);
  Serial1.flush();
  delay(37);

The flush blocks until the send buffer is empty again.  That way you don't have to account for that time and all you need the delay for is the time between transmissions.
Even better would be if those things were in an array so you didn't have to keep repeating yourself.  Anytime you catch yourself putting numbers on variable names what you really want is an array so that you can use those numbers in the program:
for (int i=0; i&lt;6; i++){
  Serial1.write(sw_binary_train[i]);
  Serial1.flush();
  delayMicroseconds(950);
}
delay(37)

looks much better.