Joe,
I cleared RxData after LCDout as you suggested with no change in results. Then I tried this addition:

LCDOUT $FE,1
LCDOUT RxData[1],RxData[2],RxData[3],RxData[4],RxData[5], RxData[6]
PAUSE 3000
Results: first pass: BABCDE. second pass: PABCDE
This is even more puzzling.
String display after first pass OPABCDE…Byte display PABCDE
String display screws up two bytes while byte display screws up one byte????

With this change:
hserin 2000,TimeOut , [wait ("A"),str Rxdata\15
LCDOUT $FE,1
LCDOUT RxData[1],RxData[2],RxData[3],RxData[4],RxData[5], RxData[6]
pause 3000


Results:
first pass: ABCDEF “A” should not have been displayed
second pass: CDEFGH
third pass: ABCDEF same as first pass
forth pass: CDEFGH same as second pass
and continues to rotate output data through each pass

If I Rx string then LCDout and END with only one cycle the results are the same ABABCDEF…..
It sounds like RxData IS clearing based on changing first display byte. So it has something to do with hserin RxData “I think”. I added a delay after Tx output with no change in Rx. Still scratching my head...........

By the way, I like your quote from the 1950's. I've passed it on to others.