Yes, 370 Ohms is not what I would expect. I would think that SDA would be the same as SCL. I have no idea what could have happened to cause that. At this point, all I can suggest is to get a new LCD with an I2C backpack. Sorry.
If you measure from Vcc to SDA and Vcc to SCL you should see 4.7KΩ. 4.7K is the value of the pullup resistors on the I2C backpack.