In a balanced incomplete block (BIB) design, what is the best way to ensure each treatment appears in all positions/orders? Should I randomize treatment order within each block, so that participants within each block see the treatments in a random order? Or, should I randomize the order of treatments in each block once (such that all participants in a block see treatments in the same order), ensuring that across all the blocks, each treatment occurs in each position?
You should randomize treatment order within each block, unless there is something special about your experiment (which you did not tell us) that dictates otherwise.
If you use your second option, results might be biased ... maybe there is some learning effect, so treatment always shown first get a disadvantage, or something else.