With the very greatest of respect.
You post that this is your first double rifle. You go to one of the best companies in the world that has been building double rifles for 150 years, and they advise you to keep it at 14-15 lbs.
Why ignore them?

Now H+H are a bespoke rifle maker and they will happily take the Ł 100,000.00 or so that it is going to cost and build it at 11lbs, but it will be a monster. It will be no fun whatsoever to shoot and its resale value will be dramitically reduced.

IMHO before you decide to lay out this sort of money try and find a comparable rifle, if not a double, a bolt, in a cartridge with similar recoil energy verses weight ( a light 505 gibbs, 460 WBY, a 458 lott in a 9 lb gun without a break spring to mind. You can calculate the same free recoil energy with "point blank" software) and fire them 6 times in sucession at the range. If you still want the 11lb 577 then go ahead.

It is not a macho question of being recoil shy, it is the practicality, it will slap you so badly that the quick 2nd shot for which we shoot doubles will be next to impossible.

Regards