Fabulous. What a relief that must be!
You know they aren't entitled to an update next year, don't you? From Section 2.7 of the DCSF elective home education guidelines to LAs:
"Local authorities have no statutory duties in relation to monitoring the quality of home
education on a routine basis.
However, under Section 437(1) of the Education Act 1996, local authorities shall intervene
if it appears that parents are not providing a suitable education."
Requiring updates from a family which, as the LA has already acknowledged, appears to be providing a suitable education would be routine monitoring and is not necessary. You are therefore finished with your LA, unless and until the law changes. I wouldn't bother telling them so until they come pestering you next year, however. If your LA is like mine and some others, it may be so disorganised that if you correspond on the subject now, you'll only have to repeat the correspondence again next year.
(BTW I also take exception to their phrase "proposed educational philosophy" which implies that the LA was in a position to approve your plans.)
Which is not to say you shouldn't be chuffed. You've clearly done a good job of explaining how you are educating your children!