When you installed the H80i did you use the pre-applied thermal compound on the waterblock or did you use your own? If you used your own did you remove the pre-applied thermal compound ? Also make sure the waterblock is making good contact with the cpu, not super tight just snug. Make sure the pump is running at 100% too.
I'd remove the stock thermal compound and use Thermal Grizzly Kryonaut, this should help lower temps a little more.
Even when mine is hitting 1.4V under load it doesn't go higher as about 80°C on Prime! Gaming is 60° max when the Water got warm. (And thats all on very low Fanspeeds). But i use a custom loop with 280mm Radiator (thin one)
Oh, i forgot. Mine is delidded and the Factory paste is exchanged. Might also be a factor.
Swapping rads around will not fix your problem. Something must be wrong there. Either the cooler/paste is not on properly or the water pump is not working. Or maybe the cooler has air bubbles inside? Although you should be able to hear a bubbly noise from the water pump if that was the case. Silly question, but did you connect the pump to a voltage source?
My 6700k barely reaches 60C under 100% load with a H110i rad. Temps usually settle around mid to high 50s under full load. CPU is running at 4.6GHz, LLC-6 with Cache at 4.5GHz and 3466MHz on mem. Voltage shown in HWINFO is 1.249v. I can't remember the exact setting I have in the BIOS but it's around 1.235v.
My 6700K under load was 55C-60C with a Lucifer V2 air cooler. Based on your temps it seems your cooler might be the issue, here. As pointed out above it would be a good idea to reapply thermal paste (don't cheap out, get a good one) and re-seat your cooler.
Couple of other things, though. What are your ambient temps? And are your CPU temperatures constant? I noticed that my 6700K had severe voltage and temperature spikes that would reach 75C-80C before I changed some BIOS settings.
Just to clear up one last thing, you mention the H80i as your cooler, but you swapped that for a Noctua NH-1 to check? Is that correct?