My other car a pretty new BMW with the latest diesel engine has no such problems with the DPF. If I have done a few short journeys it does an auto regen which makes the exhaust note a little deeper for around 20 mins other than that not noticeable. The 2.7 Jag is an older design pre Euro 6.
Diesel technology has moved on since 2003 when Ford announced the 2.7.
You are correct in that a unused car will eventually go flat. More likely in a Lexus hybrid with a small 12 battery although my GS quiescent current was 15mA so should last several months assuming the battery is fully charged. My BMW which has a huge 12v battery in comparison, 95Ah should be able to supply the 45Ma current for 20 months. Maths isnt my strong point so may have got a decimal point wrong although a collegue parked his car up while posted overseas and on his return 6 months later it started first click.
45mA = .045A so 95Ah is 87 days before flat so even allowing for only 50% should be good for 10 months. The GS assuming half size battery then 5 months. I measured the GS & the quiescent current was 15mA so well you do the maths.
Ed