Yup, that did the trick. There's a setting on the "Network" section of the profiler to set a delay. The page on the website for the Connect app doesn't mention anything about it.
Anyway, 24 hours later my TV is now calibrated via the eeColor for both my Sony bluray and my Apple TV as separate buttons with a quick 1000 patch each to get a feel for which settings for the LUTs I like on the TV before doing a full 17^3. I'll get around to my Fetch box later. Fit Chroma seems to be producing the best looking results on my LG C6, and especially with my cable box which otherwise seems to flatten the brightest areas of a picture (skies and the 20th Century Fox logo being the worst offenders).
Seeing as I can't calibrate via the cable box as an input, I see a lot of fiddling with the options to find the best compromise for that awful box.
LG OLED55C6T, Yamaha RX-A2050, Q Acoustics 3010, 3050, 3090 speakers and 3070 sub, Yamaha YST-SW030 rear sub, Sony BDP-S6500, LG UP970, Fetch TV Mighty, IQ2HD, Apple TV Series 4, Pioneer CLD-D5V laserdisc, eeColor LUT+Lightspace HTL+i1Display Pro and DreamScreen, housed in a Dataworld 42U rack & AC Infinity S9