Hi. Lifting the house up sounds ok - our hamster is quite a hide away type as well. They aren't keen on being picked up while in the cage sometimes, so when you've lifted the house up, try putting a kitchen roll inner cardboard tube (or similar) in the cage near him, with a treat at your end (your end outside the cage) and he should walk into it. Then you can either lift him out in the tube (with your hands either end), or put your end of the tube into a hamster ball so he walks into the ball. Let him have a run in the ball for five minutes or so to wake up properly and get used to being out of the cage and then take the ball upstairs to the dry bathtub for some taming. This bit might help your little girl as well.
When we did the bathtub taming, our little boy used to get in first (dry bath obviously and we put the plug in too). Then I'd put the ball in the bathtub and take the lid off. Charlie would run around and climb over little boy who was technically just part of the furniture so our hamster wasn't scared of him. This helps get them used to the scent and presence of a person. You'd need to be there too just in case Barnaby runs up her arm and tries to jump out! (A hand blocking this stops it). I used to leave the cardboard tube and ball in the bath too and when Charlie went in the tube, little boy would get out of the bath (so as not to squash Charlie while he was running around).
The bathtub is a good place to let Barnaby run around without escaping and get used to being out of the cage and a good place to start handling him until he gets totally docile about being handled.
I did a short video on bathtub taming - it's not that great and doesn't show much but gives some tips as to how we got Charlie handleable.
Timing - I would suggest waking him about the same time every night - to fit around meal times and bed times (6 or 7pm maybe) and getting him out in the tube and ball as above. But first he needs to wake up. If you put his food out and change his water bottle at that time, and clang the bars a bit while doing it, that should wake him up, then get him out in the tube/ball.
I don't know much about long haired hamsters so I'll let someone else answer the grooming bit!
Our little boy isn't nervous about holding Charlie any more except when Charlie sticks his nails in him! He doesn't do that to me so I think it's when they sense that children aren't confident handling them. Your little girl could maybe wear gloves when handling him at first (small sized gardening gloves eg), so she gets less nervous about the sharp nails and then when she's more relaxed she'll find it easier to hold him. But really it's easier to get them tamed before trying to do too much handling (so if she's in the bathtub, jeans would be a protection but Barnaby is unlikely to stick his nails out when just running around).
It took us a few taming sessions, but once we could pick Charlie up he was docile as anything and I could even pop him in my dressing gown pocked (not while walking around obviously).
They get used to the routine of being woken at a certain time. I'd say 7pm ish - nearer bedtime, is better than 6pm as they can be pretty active around 6pm I've found, but are slowing down between 7 and 8pm ready for an evening nap.
You can put towels down in the bath for a softer landing if he 'pings' (ie leaps 2 or 3 feet in the air when you try and touch him!). This is what Charlie used to do when we tried to touch him.
Once he was tamed (and it took a couple of times a week over 3 or 4 weeks, but he was feral, so yours might tame quicker), I used to get him out in the tube and carry him to the sofa and sit on it. We have a blanket blocking the edge of the sofa and his tube and a hidey place so he can pootle around on the sofa, but if he's in active mode he just keeps trying to jump off and then I don't bother. If he's a bit dopier he often just sits between two of us having a wash (high sided walls making him feel safe I guess). Or crawls under the blanket for a nap. If he does that I lift him onto my knee on the blanket to avoid the risk of someone sitting on him.
Also when he's a bit tamer you could set up some kind of playpen so he can be out in the living room or bedroom a bit maybe.
Anyway here's the video that explains how we got him used to touch. Doing it this way will also help your little girl build confidence. We didn't do the 'getting in the bathtub' at first, just the light occasional stroke on the back at first.
https://www.youtube.com/watch?v=kjyEme2xcq4