Hello Bill
I've been running the diagnostics test on a PCF8574 chip (not backpack) and a 16 x 2 bog standard LCD.
After a bit of a shaky start, I got your "Hello World" example running from the I2Cexp class (all other libraries to date for I2C LCDs including newLiquidCrystal have failed to deliver so far - might be a pinning problem though).
This is where I ventured into the diagnostics test.
I got further than the other poster in that it reported an LCD found
Scanning i2c bus for all lcd displays
LCD at address: 0x20 | config: P65401237L | R/W control: Yes
Total LCD devices found: 1
But it failed both parts of the memory test. The LCD displays rubbish. I've taken out the things that might cause problems like
// turn on ESP8266 specific pin decoding
// Turn this off if it creates issues.
//#define I2CEXPDIAG_CFG_DECODE_ESP8266PINS
and
//#define LCD_CHEXECTIME 2000
//#define LCD_INSEXECTIME 37
No difference. Any ideas?