For this, it sounds like she’d likely lead train fairly well. If she’s only gone for a short while, she probably just wants a little bit of outside time and she’d be fine. The thing about lead training isn’t that you just pop it on and let them out, you do need to stay with them while they’re out to ensure they don’t get tangled in anything or escape the lead. May I also recommend this person’s cat jackets for a harness? They are comfortable and fairly escape proof.
As for the “gifts” you may want to look into some additional toys for her that can satisfy her desire for that particular behavior. Stick and string toys and laser pointers are good for this, but a lot of people don’t reward their cats for a solid catch, which is fine, but if your cat is looking to chase and catch a thing she can eat, it may help to give her a treat at the end of playtime. This encourages play behaviors with you over going outside to do it.
As for the cat grasses, you can actually make her a little grass mat!
All it takes is a large litterbox (or if you want to do bigger, go to a hardware store and look for the cement mixing section, and they sell rectangular black tubs there- that’s what the first two tubs are at least), some clean dirt, and some grass seed without fertilizer in it (or if you can’t find that, you can plant cat grass from a pet store in the middle, it will spread but not as fast).
Again, any one of these on their own likely won’t completely solve the issue, but between the three, you may see a decrease in escapist behaviors.
As long as we’re here, @crabcakedraws asked what I say to people in apartments whose cats scream and destroy things demanding to be let out, and first you should go have a talk with @pangur-and-grim about Grim’s behavior around go-outside time. My own advice is to take the time and effort to train your cat to go outside on a lead with you. If you think that’s too much trouble and you’d rather just expose your cat to the risk of illnesses, injuries, or potential death by opening the door and just letting them out, I definitely can’t stop you. But that doesn’t make it right or good.
Think of it this way. Children, actual human children, throw tantrums when they’re not allowed to do whatever they want; does that mean parents should allow kids to do whatever they want all the time? Absolutely not, and you’d be appalled at any parent that said they did so. Even if a child screams and cries, even if they throw things or hit you, you’re still the parent. It’s still your responsibility to make sure that they are receiving the correct/best care you’re capable of providing. Don’t want to do that/think that’s too hard? I have news for you: you may have chosen the wrong pet.