Some better results!
Today, I re-plated the RE and the Bromide electrode under safelight. Now the 0.1M KBr solution gives a reading of -68.0 t -68.5 mV. Ambient temperature was 20C so according to the chart, that should give a reading of about -62.56 mV. Since my solution has sat for a few days there may have been some evaporation and it could now be at higher concentration and/or it could have been a bit off in the first place. Later this evening I will make fresh solutions and get new readings as Kirk suggests above.