We have the difficulty recognizing the key issue, which is fixed by pressing lock then unlock on the remote, as worked out by my wife (and you) who is the main driver. Also the double beep when pressing the tailgate button to close it, which I fixed once by doing the foot wave thing but which is mainly fixed by the lock / unlock sequence as well. It often doesn't recognize the foot wave as well and we have had one or two times where we noticed the OAT was not correct, but that quickly fixes itself. None of your other display problems though.
We also had the service indicator prompting for a service at around 13,000km, which I complied with because there is no way I am going to go further than that between oil changes anyway, no matter what LR says. The dealer said it was wrong and they would reset it but I disagreed and got it serviced and then they reset it. 
We don't have any DPF regen issues because my wife drives significant distances at reasonable speeds most days of the week.
We haven't approached the dealer because none of the issues affect the drivability, once you figure out how to get the car to recognize the key and get the boot shut. I would rather drive it than spend heaps of time at a dealer! When we do the next service next year I will tell them about the glitches and hopefully by then they will know how to fix them after fixing your car and others!
I note that my L405 Range Rover did the double beep thing when trying to close the tailgate when the key was accidentally left in the house, so I presume that the DS is not recognizing the key when it does it and pressing the lock and unlock button on the remote should probably fix it.
I will follow your post with interest to see if you end up with a satisfactory fix.
FYI, watch John Cadogen's video on DPF's and you will see how important it is to drive adequate distances regularly or you will be up for a very expensive new DPF. This is not a Land Rover only issue. In your position with two regen messages close together I would be going for a few hundred km drive in the country on the next weekend to save the DPF. Can't be much of a chore in Tasmania!
				
			 
			
		 
			
				
			
			
				Bob
2010 D4 3.0TDV6 SE, ediff, LLAMS, 5 x GOE wheels, LT285/60R18 BFG K02's, GOE Compressor Guard, LR Tank, Mitch Hitch, ECB Bull Bar, Kaymar Rear Bar, Traxide, Safari Snorkel.
2019 Discovery 5 SD6 SE, 20 inch wheels, 275/55R20 Nitto Grappler G2 tyres
			
			
		 
	
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