Brian,
Our LR3 does something similar, it has a slight shudder and makes a low noise when slowly accelerating from 70 to 75. I found this over on rangerover.net and it seems to cover our problem and it sounds as if you have the same issue.
No: LTB00010
Issue: 1
Date: 15 Jan 2007
Poor Acceleration from 62 to 75 mph
AFFECTED VEHICLE RANGE:
LR3 (LA) (V8 Only) VIN: 5A000360 to 6A413981
Range Rover Sport (LS) (Normally Aspirated Only) VIN: 6A900129 to 6A983116
New Range Rover (LM) (Normally Aspirated Only) VIN: 6A194480 to 6A239035
CONDITION SUMMARY:
SLOW ACCELERATION AFTER CRUISING SPEED
Situation: With the engine at normal operating temperature, a customer may report very slow
acceleration from approximately 62 to 75 mph (100 to 120 kph) after steady cruising. A customer may
also complain about a low frequency cabin boom type noise and vibration when accelerating in this
speed range.
Action: Should a customer express a concern, refer to the Repair Procedure detailed in this bulletin
to re-configure the Engine Control Module (ECM) using the Integrated Diagnostic System (IDS).