I'm not familiar with 'find my phone' apps -- they use GPS?
So the police could send a copper out with a cheap used phone from a car boot sale and stick a sim card in it, stick it in the same bin at 3 am on a Saturday morning, wait for the bin lorry, and then keep pinging the phone with the 'find my phone' app and see what comes back to them? They could also glue a note onto the phone's screen and leather case (with the phone in a case) saying "call this number if you find this phone/case" and wait and see if they get a phone call and then question the person who found the phone/case and check it's condition after a trip in a recycling bin lorry. If no one phones, that might be because they chose not to, or it indicates the test phone is not discovered during sorting.
But if those 'find my phone' apps need gps turned on, then I'm not sure how you'd do the test for a phone with gps turned off?
And if it's that important to the family and the police can't run a test like this, then the family have some money and this would only cost a few tens of quid for the used phone, sim cards can be got for free, if one is necessary, and petrol money to the horseshoe. I would personally want to replicate conditions with the timing of the bin lorry if possible...and traffic conditions and atmospheric conditions will be different at night compared to in the daytime.