I have a Cornish cross who's about 18-20 weeks now. We got her as part of a trio from some people who didn't know what the breed was, and then was horrified and couldn't cull. We culled two, and I held off on culling the last one because she had been being bullied by the rooster and I wanted her to have a few good days before she met her end.
We got the weight off, somewhat, by penning her separately during her quarantine period and she didn't get a lot of treats.
She was still very fat and I thought, not healthy, but I allowed her to sleep separately from the other chickens in the workshop and came in one night to find that she'd jumped up 3 feet to get at where we kept the mealworm bag. I figured if she was healthy enough to do that, she could live for awhile more.
She's had a respiratory infection (treated with antibiotics,) a throat tear from going up against a rooster (who got his beak sanded down for that,) laid a couple of sad looking eggs around 16 weeks and then not again. I'm pretty sure she's head hen, at the very least, in her mind if not in 100% reality as my crew is still very young.
She's currently spending her nights in a dog crate because she still wants to jump on the workshop table at night and lay massive shits. I mean, horrifically large. And this way I can leave out food for the ducks who sometimes sleep in there without her eating it all.
She runs around half the garden (I don't think she really likes trouncing through the high overgrowth of the tomato vines like the others do) and the entire stretch of gated lawn and bears a very striking resemblance to Maid Marian from Disney's Robinhood, especially how she runs.
I do know she'll have a shorter lifespan, but that's okay because it's still way longer than she would have gotten. She gets a long with bantams, babies, cockerels, and the other pullets. The rooster was the only one she truly messed with, except for those who deigned to try to get to close to her when she was eating "her food" and mainly it would be a squawk, an air peck, and then back to hoovering food, often with the same chicken hoovering alongside her.
I say all of this to point out that I do think, if you want to keep the breed, to expect 1-2 year lifespan at most, and likely for them to have more health issues in general. If you can't cull, then I wouldn't suggest it but then again, most people who get CornishX aren't sending them off to processors, and definitely aren't sending off one or two.
I personally wouldn't necessarily mind culling her (we are downsizing, so picking favorites and everyone else is going to Camp Freezer, and her poops are SO big and a pain to clean up when not in litter) but two of my household love watching her run her bag of bowling balls ass up to the gate. And she is a crowd favorite with anyone who comes to see the chickens.
It is possible but you do have to keep the weight down which means creative ways of feeding, and heavily encouraging foraging. If you have them with limited space in a run, I would just suggest looking her over regularly for any scabs that look like bumblefoot, or any pressure sores on her chest. The first hen we culled (who's been acting completely normally from what we could tell) had a horrifically sized abscess covering the whole front of her torse. She looked completely normal, even culled and plucked but we decided to check out a small, pencil eraser sized circle on her lower torso. So much squeezing and flushing pus out that we opened her up and it was practically stem to stern (I have a picture if anyone wants but it's graphic.) She had to have been in SO much pain.
We pick our's up a lot and look around her belly but we need to do a better job. She never seems to be in pain, even when handling her. Mainly she just seems pissed off that we're deigning to handle her highness without giving worms.
There's an old member here on BYC who bred "roads" which were taking Cornish crosses, keeping them slim(ish) and then breeding them to heritage breeds for interesting F1 generations. I would recommend looking those up.