I was advised against the 276/75s and went for 265/70 BFG ATs on mine, basically standard height vehicle.
The speedo will change - but the speedo's accuracy is fairly meaningless, if you want accuracy on the vehicle's speed, use a GPS device. What is more important is that the odometer - accurate from the factory on factory tyres - becomes inaccurate. You will be doing more km than shown, so if you're finicky about regular servicing, wipe a few k's off the indicated figure (over 10,000km, you could see over 100km difference). It all depends on how specific you are, I suppose. Personally I don't really care a few % this way or that, I don't thrash my car anyway.