I’m honestly not sure what the best course of action is. There is a [name_u]Berry[/name_u] on here who has a rather large family (several of her children have double-barrel names–[name_u]Kelsey[/name_u]-R0se, [name_f]Soph[/name_f]!e-Cla!re, J0hn-P@trick, M@ry-[name_f]El[/name_f]!zabeth, and I think even S@rah K@therine. Most of the ones with double barrels have hyphens, but I don’t think S@rah does.), and it seems to work super well for her. I remember her saying once in the past that some try to call [name_f]Soph[/name_f]!e-Cla!re just [name_f]Sophie[/name_f], but quite a few seemed to stick to the full S0phie-Cla!re. Then again, seeeeeveral years ago whilst I was interning for my university degree, I met a pastor and his family, and their son (only child) was named [name_u]Michael[/name_u]-[name_m]Kellan[/name_m]. I’m not 100% sure if it’s hyphenated or not, but I do know that they intended for him to go by both. Apparently it was like pulling teeth. NO ONE would call him the full [name_u]Michael[/name_u]-[name_m]Kellan[/name_m]. It is a little on the long side, so I guess I can understand, but still, I at least TRY to follow the parents’ wishes. But I guess a lot of people just didn’t “get” it. 
I love [name_m]French[/name_m] double barrels that start with [name_f]Anne[/name_f]- ([name_f]Anne[/name_f]-[name_f]Sophie[/name_f], [name_f]Anne[/name_f]-[name_f]Claire[/name_f], [name_f]Anne[/name_f]-[name_f]Louise[/name_f]–[name_f]Anne[/name_f]-[name_f]Louise[/name_f] is currently on my list!), and I love the versatility of it. She could be [name_f]Anne[/name_f]-[name_f]Louise[/name_f], just [name_f]Annie[/name_f], or even [name_f]Louise[/name_f]/[name_f]Lulu[/name_f]/[name_f]Lula[/name_f], etc. (I’d pray to avoid [name_f]Lula[/name_f], as I am not a fan at all, lol, but I’d be happy with [name_f]Annie[/name_f], [name_f]Lulu[/name_f], or [name_f]Anne[/name_f]-[name_f]Louise[/name_f]! Similar with [name_f]Anne[/name_f]-[name_f]Sophie[/name_f] and [name_f]Annie[/name_f], [name_f]Soph[/name_f], [name_f]Sophie[/name_f], and simply [name_f]Anne[/name_f]-[name_f]Sophie[/name_f].) I also love [name_m]John[/name_m]- double-barrels, too, especially since [name_m]John[/name_m] is a huge family name, but yeah, I think the beauty of double-barrels are the options!
But I can see your point–if [name_f]Amelia[/name_f] felt naked without [name_f]Jane[/name_f], I’m not sure I’d be happy people were calling her just [name_f]Amelia[/name_f], or even worse, just a nn for [name_f]Amelia[/name_f]. 
Personally, as someone who religiously sticks to two middles, I plan only to use one middle with a double-barrel. Like… even [name_f]Anne[/name_f]-[name_f]Louise[/name_f] [name_f]Eva[/name_f] [name_f]Kate[/name_f] seems inordinately long. Like, WHEN DOES IT END ALREADY!!! lol. [name_f]Anne[/name_f]-[name_f]Louise[/name_f] [name_f]Eva[/name_f] still gets three names total, which I think is just fine.
That means I want that middle to REALLY count, though!
As for hyphen vs. no-hyphen, I am pro hyphen. It seems much more obvious that [name_f]Amelia[/name_f] and [name_f]Jane[/name_f] are supposed to be used together, and I think [name_f]Amelia[/name_f]-[name_f]Jane[/name_f] [name_f]Autumn[/name_f] is gorgeous! Plus, it sort of helps to clear up how the name is supposed to flow. Maybe it’s just subconscious, but I think [name_f]Amelia[/name_f] [name_f]Autumn[/name_f] [name_f]Jane[/name_f] sounds much better if there’s no double-barrel, but if she’s going by [name_f]Amelia[/name_f] [name_f]Jane[/name_f], I think [name_f]Amelia[/name_f]-[name_f]Jane[/name_f] [name_f]Autumn[/name_f] sounds quite different? [name_f]Amelia[/name_f]-[name_f]Jane[/name_f]/[name_f]Amelia[/name_f] [name_f]Jane[/name_f] is almost said like one unit, and therefore I don’t find the transition between [name_f]Jane[/name_f] and [name_f]Autumn[/name_f] to be so harsh. Maybe I’m just losing it, though. 
Good luck!