Tactical 4x4 makes a 3/16" steel bracket for the new AMK pump, designed to lift it up just enough to clear their own sliders (side-by-side comparison with the stock aluminum bracket included with the AMK retrofit kit and standard issue on MY2012s and newer LR4s):
When mounted under the car, you can see the fairly significant clearance difference compared to the chunkier stock bracket setup. Old:
And new:
Coupled with the "box" welded on their driver's side under the compressor, that bracket yields enough extra clearance to barely (maybe by couple of mm) allow the sliders to be bolted up while avoiding vibrations and noise from contact. Unfortunately I heard from owners of Rover Specialty sliders - similar desgn as the Tactical - that this bracket helped, but not quite enough to clear their design (don't know which ones you have on your LR3.) Worth a shot though, as the bracket is probably inexpensive from the Tactical guys. Even with their sliders, the lower acoustic cover has got to go, but the AMK unit is so much quieter than the Hitachi one, you can barely hear it running anyway after the sliders are installed - as long as there is no contact between bracket and slider. Otherwise, it makes quite a racket.
My understanding is that a new compressor relay comes included with the AMK retrofit kit along with required fittings, bracket and acoustic cover. The only thing needed after replacement is a software update to the EAS control module, since the operating strategy of the two compressors is different.