Hi, first time poster here. I've read a ton of topics about this, but hope someone might have suggestions for my specific situation. Hopefully this isn't too long - I just wanted to provide enough details 
Hamster: I adopted a female Syrian (she's 5-6 months old) about 3 weeks ago. I hadn't asked about any issues, but was told she wasn't tamed and hadn't been held or handled very much. From what I can tell, she's sweet and very curious (hasn't bitten me or ever seemed aggressive), but I'm also having a hard time understanding how to keep her entertained and happy.
Cage/Taming: She's in an Ikea detolf and seemed to be doing well at first. Very skittish, but got used to my voice and me being around in about a week. I let her settle in for the first 3 days, put tissues with my scent in, and after that, tried leaving my hand in a couple times. At the start of the second week, she took a treat from my hand (but it's only happened once so far). The detolf is probably 3-4x larger than what she was in before. There's a side of the cage filled almost to the top for burrowing, a multichamber, cork logs/tunnels, two hides (one ceramic), sand bath, silent spinner 12" wheel, dig pit with coconut fiber and chips, a smaller container with aspen, toilet paper rolls, whimzee/other wood chews, and I scatter feed. Part of the top is covered with a DIY wire lid that's raised a little bit to fit the larger wheel in. I haven't cleaned her burrows/nest yet or done anything more than spot clean. She burrows deep down in the bedding and sleeps there - doesn't use any hides.
Playpen/Free Roam: I tried taking her out to a playpen area (it's foldable, kind of looks like a honeycomb shape) around the second week. She took to it pretty quickly. The only problem is that she learned to scale the sides of the playpen, so it has almost become unusable... 
She'll play around with the stuff in the playpen for 2-5 minutes, groom, maybe run on the second wheel in there, then keeps trying to escape by climbing the sides... So I hamster proofed my room and let her run around there, instead. She's done that a couple times now in the second/third week and really seems to enjoy it. However, she's started chewing at the carpet and biting the corners of heavy books I'm using to block holes. For now, I just bought those plastic cube containers to try and create a DIY fence - then I can have her out on our wood floor in a slightly less escapable, hopefully easier to monitor space... 
Problem #1 - Chewing: So the issue I'm having is that as soon as she wakes up, it's become a routine for her to run in the wheel for a couple minutes, then jump out and run over to bite at a couple spots on the lid. There's a specific corner she tries to climb up using a hide nearby, as well as another edge above her kebob/dangling chew toys where she gnaws at the lid for several minutes at a time. I recently discovered that she's also biting the metal bars along the bottom, especially where her nest is/opposite her nest. The coating to the metal is gone in one spot. This morning, I watched her biting away at it half asleep - her eyes were actually closed!
She wasn't chewing the lid at all before I gave her playpen time. It's almost like she didn't even realize there was a "top" to the cage before that. But now she's absolutely fixated on getting out... Did I introduce play time too early? Does she need more time to settle in, or is she simply bored and unhappy with the cage?
I've tried:
- Giving her more free roam time. I can't do it every day, but I've done it probably 2-3 times in the last 4 days since she was escaping the playpen. (I hope I can do it more often once I get the plastic cube fence thingy and can have her in my living room instead of the bedroom.) The last time I free roamed her, she was out from midnight to around 1:30 AM. As soon as she got put back in the cage, she was climbing the sides and trying to get out again... I'm worried that she'll never be satisfied with being in any kind of cage. I haven't been able to drain her energy yet. She wakes up between 12-1 AM, so I'm pretty limited to 1 (maybe 2) hours of free roam time before I need to sleep.
- Reducing the bedding in some of those areas and trying to move the hide she's climbing on. She still manages to reach the top metal bars of the detolf, which then lets her eventually get to the lid.
- Putting cardboard over the areas of the lid she's getting at the most. She tears up the corners of the cardboard in a single night. It's not completely gone, so she must stop chewing at some point, but seeing shredded up cardboard is still distressing.
- Putting in more wood chews, food-based chews, homemade treats, whimzees, dog biscuits, etc. She'll nibble at them here and there and will be more interested in things like rice pops or crunchy treats, but mostly ignores sticks or chews meant for hamsters. Peanut butter trick works for a minute or two.
- Adding more toys and boredom breakers. She either doesn't touch them or isn't interested enough to get to the food inside. I've even put her favorite whimzee (not the alligator - she likes the stick-like XS puppy ones) in a toilet paper tube with the ends folded in. I could tell she was biting at it so I made the hole bigger, but even after 3-4 days, she just stopped trying and let it sit there...
- Blocking the metal bars. I've used cardboard with apple sticks glued to them. I haven't put these in her nest area yet, but a different part of the cage. I'm also going to try paper straws or bird bagel chews because they're a bit thicker and may take longer for her to chew through. Not sure how this will go, but really feels like a temporary stopper rather than a permanent solution...
Problem #2 - Taming: I feel like the playpen/free roaming is actually setting back my ability to tame. I can't tame her in the cage at all because as soon as she hears either me or the lid, she's practically jumping to get out. Maybe once out of the times I've lifted the lid, she sat quietly in her wheel and sniffed at my hand. Since having playpen time, it's just go-go-go... I've been transporting her using a Starbucks Venti cup and she's picked up *very quickly* that when the cup comes in, she gets to go out. I feel guilty being in the same room without letting her out immediately (my 'office' is in the same space and sometimes I work late or watch shows there), and I get the feeling she's chewing more when I'm around... 
But then, when she's free roaming, she mostly avoids me or will skip-jump over my hand, etc. She has sniffed around me before, but she has yet to take a treat from me during free roam time (though she did do it once in the cage). It's also getting hard to "catch" her because she isn't tame and understandably doesn't trust me yet. Is it okay to keep doing free roam time in this case? I'm really wary of doing the bathtub thing because it's a small space and I think she wouldn't like having to crawl over my legs vs. explore a wider space on her own terms. I imagine the bathtub would get the same reaction as the playpen. Does free roaming still eventually help with getting a hamster used to you - or would I need to be more proactive in the interactions?
Possible Solution - DIY Cage???: I've seriously considered commissioning someone (or a woodworker or something?) to make a DIY cage. I don't have the car or tools to get it done myself, but I can definitely pay for it. That's the only thing I can think of that would possibly solve both my problems? She'd have a larger space, and I'd be able to hand tame inside the cage since she wouldn't be able to reach the top. I'm thinking 2 feet wide, 2 feet tall (maybe a little taller), and 5 feet long. Would that be big enough? That's 1440 inches of floor space compared to the detolf's 960. I wanted to make sure the cage could fit through a doorway if I ever need to move or rearrange furniture.
Is it possible she'd still bite at the corners of a DIY cage, like strip the wood? I'm debating if it's worth the investment and wanted a second opinion. I'm also not sure where to start in terms of finding someone to make this, so any tips would be appreciated! I don't know anyone in my area (DC) who also has hamsters Thanks, all.
)) 
