I am a rescue organization and foster based, so I don't have hands-on experience with using cages like that; however, if you wanted to continue using those cages (for quarantine/sanitary reasons) I wonder if you could add (zip tie, etc.) a plastic sheet/barrier to the door, to prevent their little legs from getting caught. Depending on the age/mobility of the kittens you may need to put plastic on the whole door, but then you could just cut little holes out for ventilation.
I use these for young kitten pens, which might be another option:
https://www.amazon.com/Tespo-Playpen-Portable-Plastic-Transparent/dp/B06XTG94TH/ref=mp_s_a_1_8?crid=HFO3OTP6RA7I&dib=eyJ2IjoiMSJ9.BjycYoXC0e5DoiDRbfOBcsd4ROIxDL5HkGTKeR6J1uvWByQEZ5UsgkXU0_fhT5A3gSIjdtidA5kQhnxaU3Pe0vLUVgVQ69IU65xq1HvAlkwSXdg7PAcjuwroHBdtYK-FH-J1M-6zOxIks6NirftQeRLBvy_HM2jyjbvY5nWxlwGUYyL-hc7i6xy7Yv6GAFuPlWAITBC4UmpjurUI-z1ckQ.T2YSu4DEcchv4H5qOk4ziZJ7naXXQEJj4fzx4WqGntw&dib_tag=se&keywords=plastic+pens+for+cats&qid=1708676217&sprefix=plastic+pens+for+cats%2Caps%2C153&sr=8-8
There are also pens from Clearly Loved Pets, but they are pretty pricey and probably wouldn't be as practical for a shelter environment if the kittens are still in the quarantine stage of their stay with you.
https://clearlylovedpets.com/
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Kelly Gendreau
President/Founder
LEASH Animal Rescue
CA
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