Yeah take the EEPROM out of the picture to begin with.
And I'm not sure about the way you're sending the values back to the PC. From the PC you're sending as ASCII and in interpreting it as 2 digit hex values (each preceeded by an 'a'). You're storing the values as bytes. Then you're sendng them back as a raw (binary) to the PC. Is the terminal program then setup to interprest the value 20 as 14(hex) or how is it supposed to work?

Code:
FOR d=0 to 63
   HSERIN [wait ("a"), hex2 H[d]]
NEXT

FOR d = 0 to 63
   HSEROUT[H[d]]    ' Send raw byte values
NEXT

' OR...

FOR d = 0 to 63
  HSEROUT[HEX2 H[d]]    ' Send ASCII text representing the values as two hexadecimal digits
NEXT

' OR...

HSEROUT[STR H\64]     ' Send string as raw values