Keep in mind that many secure no-cell-phone zones, even those that host classified data are still relatively physically open. The personnel allowed inside them are strictly vetted and trained to be self-policing, but it's only the threat of discovery and harsh punishment stopping someone with the right badge/code from physically bringing in a phone. There generally aren't TSA-style checkpoints or patdowns. Happens accidentally all the time, especially in the winter with jackets.
Can't you have one or more x-ray tunnels or other scanners? They don't even need to be actively monitored, just treated like CCTV.
This is misunderstanding the purpose of the restriction.
The main reason not to bring a phone into the room is that the phone could be compromised. If the person is compromised then a device isn't your problem, because they could view the documents and copy them on paper or just remember the contents to write down later.