jboyton,
Thanks for that - it now works as you described using one BMP180!
So, based on your input, is it fair to say that the pin numbers used in the original script (2,3,4 & 5) correspond to UNO digital I/O pins by the same names? I assume yes.
Next, I added a second BMP180 to pins A4/A5 and modified the sketch to those pins...and it now works perfectly.
Thanks again for the assist!