Some ideas:
1. Do a Live Lounge cover - things like these seem to really build a lot of goodwill, specially in the UK. Sam Smith's "How Will I Know" for example brought him into a lot of people's radar. She could cover one of his songs like "Restart" or "Like I Can" , there would be no pressure for it to be a hit, would be a comfortable setting for her, and will hopefully be shared a lot in social media.
2. Start her new single promo in the UK - American charts now seem to take notes from other markets before a song becomes a hit there (See "All Of Me", Sam Smith etc) It also seems that it is easier to achieve a hit in the UK by having really good visibilty/promo. She can do three solid weeks of doing UK promo and then bring the campaign to America. Even #Beautiful was a decent hit there considering she didn't even fly to the UK last time.
3. Cross promote - Do album tours and concert tours at the same time. Coldplay does this a lot. They do one small paid concert show for most major cities. and will often times even film it. It excites fans, works financially because the costs of logistics are shared, and again there isn't any pressure for the shows to be a success. One concert in London, Paris, New York, Tokyo, Sydney. She can use this material should she decide to do promo for a full tour in the future.
4. Make better use of her social media. Can you believe that not one of her TEC tour performance official footage is on her channel? The ones where she actually sound good should be the ones uploaded and shared and not leakage from bad performances. She has those footage, just upload it.
5. An uptempo this time please Mariah. A good old school easy to sing along uptempo. This formula has had a 100% success rate so far with her lead singles. Time to bring it back.
6. A better team, and perhaps a make over.She is in ball gowns all the time and it makes her look a lot older than what she is. There are a lot of talented and up and coming people there who would even probably work for free for some recognition. Be it a make up artist/photographer, designer, director. Heck the lambs will most of the time create better artwork than her official team. The possibilities are endless, she just needs to be more open to working with people who aren't established yet.