It's not the I2C that's slowing things down, as the ADC supports high speed coms if you set the right registers. So I think(?) 860sps is a hardware limitation elsewhere. If you had multiple ADC's and synchronized them at the start of a sample run with some well timed resets, you could probably interleave the readings. Getting sensitivity of 0.0078mV with so little effort is nice, but I don't know what it's power consumption would be in a logging application. (--insert recursion joke here--)
Those spikes are primarily from waking up the processor long enough to read/reset the I2C device registers, and in the RTC event, sending the interval sample data to an AT24C256 eeprom which buffers for a few days before the SD card dump. Power consumption on the loggers is very stable unless they are interrupt driven, so the drip sensors can burn through batteries much more quickly if they are constantly being triggered. But we still get at least 8-10 months out of them. The SD cards are the real power drain.
I have not really investigated wireless transmission yet because most of our loggers go under water, or far underground. We just save everything on SD and swap the units during service visits. Though I do have a few Moteinos ready to play with...if I ever get that far into the never ending todo list...
I just did this test to see if it was worth adding the ADS1115's to a field instrumentation course that my wife teaches, and the serial plotter (which I had largely ignored up til now) was just a nice bonus.