Does anybody have experience with the Rohloff, Nu Vinci or Shimano auto shift or automatic transmissions systems on powerful ebikes?

What exactly do you want to know?
I'd try it once at the eurobike 2015, was great
But unless it's a fully automatic gear, you should give the shifting always a second time without pedal power.
r-m.de/en-en/technologies/shifts/
r-m.de/en-en/e-bike/supercharger/supercharger-gt-nuvinci-hs/#18X04_26010507
r-m.de/en-en/e-bike/delite/delite-gx-rohloff-hs/#18D10_05020709

I guess yo already know this page:
bosch-ebike.com/us-en/products/eshift/

The Rohloff and NuVinci are not automatic transmissions, they are internally geared hubs (IGH). While they do work with motor assist, their usage with "powerful" ebikes is somewhat limited as their power-handling is designed with human abilities in mind.

Do not recall reports of success with much over 500 watts on any long-term basis. Expensive equipment to find the breakage threshold for.

I believe that Eugene CAT is using the Nuvinci hubs on their pedal assist cargo bikes with good luck so far. They've torn up other drive configurations.

It is a Continuously variable transmission (not automatic), because it would be manually activated.

There are "autoshift" drivetrains for bikes, but I haven't heard of them also being used with power assist. A couple of companies have also been working on Autoshift for Di2, again not EV specific.

Both Rohloff 500/14 and Nuvinci NH380 can be fittet with an additional automatic controller.
https://www.rohloff.de/en/products/speedhub/e-14/
Harmony? / Harmony? H|Sync? | Fallbrook Technologies Inc.

Bosch has fully integrated the Rohloff 500/14 into it's CAN-Bus, as well as the Nivinci Harmony H|Sync.
So a shifting command (wheater it's automatic initialised or manually started) first reduces the motor power before starting the shifting process.
Same with Shimano Nexus Di2 and Shimano Alfine Di2 automatic gear hubs on Bosch bicycles.
https://www.bosch-ebike.com/us-en/products/eshift/

I've ridden the Shimano and Nuvinci. Haven't tried the Rohloff yet. The Nuvinci was pretty amazing actually, although reports seem to indicate it is very sensitive to correct setup. While nice, the auto-shifting systems seem to create a feeling of disconnect from the cycling experience, at least for me. Might just require some more time on the system for it to start feeling more natural.

So what's your plan?

I'm thinking your right the variable transmissions just might feel very "un bicycle". I have not tied one yet but will soon.
The bike I'm getting is too powerful for the cvt set up.

I'm either getting a Luna Cycle bike or a Vintage Electric Cruz.

Thanks

With high power you almost don't need pedals as they become superfluous as you get going very fast. Are you going mid drive or hub drive? If you are thinking hub drive I would suggest a fairly low gear ratio for the bike as you will want to be able to pedal if the battery is dead and you are hauling around a Heavy battery and motor.

Other things to consider is whether you ride alone or with a group and whether you ride for the exercise. We always ride for the exercise and I put a small heart rate monitor on my bike. When we ride in a slow group, the electric goes off and I drop gears to keep my cadence around 60. This way I can control my heart rate and keep it either in the fat burning zone (on very slow rides) or in the aerobic zone.

Sorry I didnt see this earlier. Tempo has a line of bikes with fully automatic gear hub. They dont name who the manufacturer is in the list of specs. I have ridden their bikes many times and they are impressive. Any of you who have gone to the e-bike expos know about the ramp they created to have a simulated hill to climb. A lot of people still screw up trying to climb it by not having settings correct or being in the wrong gear. For a test I stopped at the bottom, and effortlessly pedaled up the ramp. No problem! It was pretty cool. You just get on and pedal.

I will be adding their line of bikes to my store in the future.

-SP

I have Rohloff on an ebike and let me tell you, it's not all smooth sailing. There are plenty of issues at high speeds and situations where motor spins too fast without traction and then suddely catches traction: the chain comes off

Why complicate a simple thing. With motor assist the guy pedaling the bike does not need exact gearing.----You need exact gearing---very close ratios when you are riding with a pack of riders that are going near your top speed.

With electric assist for riding at 20 mph I could do just fine with a one speed 42/11 or 48/11 gearing on 26" wheel or 29" wheel. I have 9 speed gearing with a bbs02 but when riding with assist I just leave it in high gear. No real need to shift in moderate hills and city riding.