Have never had any starting issues with either the "old" 3.6 TDV8 or the "new" 4.4.
The extra capacity required to run the FBH for 30 minutes rather than 20 is tiny. I reckon less than 2 ApH.
But LR think their new battery management system improves fuel efficiency, and there is a danger with it that when you park on your drive / garage etc, the battery may be on its knees. so if you were to then ask it to run an FBH it may not start....someone in the battery / charging design part of LR did not realise these cars have FBHs.
so they knobbled them completely for the L405. Better to have cold cars rather than non starters.
cost of extra battery? not very much. some people on this forum have self installed.
cost of larger battery ? diddly squat. bit like my FBH performance.
why you can't have warm cars that also started like in my LR10......i don't understand.

Am not surprised you have been given the run around by the dealer - they wont get any help from Gaydon, and are told to fob you off - well this is my experience and what a dealer principal from a well known dealer told me.

shame really, because when working properly the FBH is a FANTASTIC piece of kit.

solution if you are out of warranty is.....(and my LR11 went out of warranty this week)
install 110ah battery
change timing of FBH back to 30 mins using IID tool.

bit i don't know how to tell the car that I have installed a new bigger battery, which dealer tells me is required. maybe i will ask an Indie to do it.

Would you please let me know if you find an Indy that can undertake this work?

Thanks, Andy 2017 4.4 SDV8 Autobiography

loads of info on this on the forum , Inc the battery module replacement recall type issue and the Gel battery recall/service action , also do you not need to turn the temp dial up on the inside of the car on 210 onwards models ?

My 2011 had the recalls done and still had the problem , luckily good dealer support found the problem which was a multi block connector under the bonnet on the charge circuit i think that was a poor connection in the block they replaced the block as it seemed to be a crap moulding on the plug and hey presto no more issues  Far to many gone...

Hello tboner001

when you say you had "the problem" under the bonnet, is what your wife / girlfriend was saying to you?

sorry...but seriously now, when you say "the problem", which one would that be as there were a few...low battery, only cold air coming out, running for 20 minutes with only warm air rather than hot.....

low battery and of course FBH would not run.

on the heat side my 2008 3.6 just heated without an issue or seemed to, my 2011 car you needed to make sure the heat knob was set to 20" , always wondered how FBH works in that respect because of course the systems also does remote vent which is cold air in hot air out ? Far to many gone...