It sounds like you're doing all the right things. She may have had a bad experience with handling before you got her. Our Robo is like that and I know he had some bad experiences with handling as a baby before we got him. Can't compare really as Robos are less handleable anyway.
Playpen sounds better than bathtub if you have one
They do try and escape lol. I would suggest persisting with the stroking on the back with one finger. Just once or twice each session she is in the playpen, without trying to pick her up. No they don't like being held too long if they're high up - both our syrians, who are not biters, have given me a little nip if I've held them up in the air too long or carried them that way, so I usually carry them in a tube or hide they've walked into, to get to the playpen.
If she doesn't get up till midnight, then that is their most super-active time! And handling would be very difficult at that time. It might be an idea to tempt her out when you put her food out. If you put it out at a certain time. I found with our last Syrian that at 6pm ish he was super active. But if I left it till around 8pm he was quite docile and even a bit dopey! He also wouldn't come out voluntarily so I used to put a tube in front of his house door with a treat in the far end and lift the tube out when he walked into it - worked a treat. Put both hands over the tube so they can't fall out as you're lifting them out.
I'd then put the tube down next to the cage inside something eg a large box - to carry him to the playpen area. Easier to put one end of the tube in the ball and let them walk into the ball and pop the lid on. Or if your playpen is in the same room and not too far to walk wiht her in a tube then straight into there?
So maybe if you can get her in the habit of being taken out around the same time early evening it would help, and then leave her in when it gets to midnight.
They are "crepuscular" rather than strictly nocturnal, so although asleep most of the day, they aren't awake all night. They may wake early evening but then nap later in the evening and also nap at some point during the night, and will be awake early morning. 11am does sound quite late though.
Sorry for the list! You already have the bendy bridge and sand. So a corner litter tray and a house would be good. You don't need to buy a wood house, you can make a shoebox house. It's a good size. Didn't suggest it before as you said she destroys cardboard! But you could try that first and maybe get a wood house later.
So cut the base out of the shoe box to be open underneath and sat on the substrate, and keep the lid as the lift off roof, then cut a hole for a door near one end of one of the long sides, with the bendy bridge over the door.
The only reason I think it's good to get the corner litter tray is they do seem to move their pee area inside the house when they have a large house - they seem to like having an ensuite bathroom!
She needs plenty to do at night being so active. With a lot of substrate she may busy herself digging tunnels and they like building mountains with the substrate too.
The design of your cage, with a pull out tray, probably isn't helping. The tray won't be deep enough to do a substrate clean that way, and still have enough substrate. When I've looked at those cages I always thought I would ignore the tray, and treat it as a tank and just scoop substrate out from the top with a dustpan into a bin bag (when the hamster is out of the cage!).
That will disturb and stress her, hearing and seeing her cage being "tinkered with" I reckon. I find it helps to have the hamster in a different room when doing anything other than spot cleaning - so they can't hear or smell you doing something to their cage as they get a bit anxious about it sometimes.
That can be tricky as you also need to keep an eye on them. I used to put ours in his pet carrier in the bedroom with a blanket over the top - it's a large pet carrier. He woud just go to sleep in it. Our current syrian doesn't like that and tries to chew out, so I put him in his playpen in the other room, if someone else is in there to keep an eye on him.
He goes very subdued if he can tell I'm doing some changes to his cage. And sits in a hide. Whereas normally he'd be running around or trying to escape.
It's trial and error really to see what works with her. Do you sit in the playpen with her? They can get used to you when you do that and tend to climb over your legs etc as if you're an obstacle. Legs aren't as threatening as hands! You need to keep well away from the edges though or she'lll use you as a ramp!
I would maybe focus on getting her into a regular routine of being taken out at the same time of evening, maybe every other night, feeding at the same time each night and turning the lights out before she gets active at midnight (if possible!).
If she's making a racket at night, then earplugs?! She might be better with a regular routine.
I'd try the large house asap though if you have a shoebox lying around. Sometimes they don't destroy the cardboard if it's their house. Keep giving her plenty of other cardboard items to destroy! Old egg boxes or kitchen roll inner tubes (slit those down the side so she can't get stuck in it) and toilet roll tubes.
You could also make her a treat parcel now and then maybe to keep her occupied - have you seen the video of 10 toilet roll toys?
Sometimes it's just finding something that works for them so they're happy in the cage. For our Syrians it has always been a large dark house and a good depth of substrate, plus overhead cover so they don't feel too exposed. You already have the shelf. Plenty of hidey places (eg tissue box) and tunnels at floor level can help, or an upturned rat sputnik eg. And bendy bridge tunnels.
If she only has a couple of inches of substrate she probably won't be happy. You could have split level so one half of the cage about 6" deep and the other half 3" ish, so you don't use as much. But best thing would be buy a big cheap bag and bung a load in!