Unfortunately magic, I can't speak on behalf of the SP's and their protocol regarding this kind of issue.
For example, your neighbours could all be with different SP's, which means there would be no 'common point' if they were to all report their DSL as faulty. By that I mean each 'fault report' would be classed as unique, and not commonly related to another circuit off the same PCP/DP. Therefore by trying to request a REIN engineer on what would probably be the first fault raised by your neighbours, I would imagine a bog-standard SFI task would be created.
However, lets say your neighbours each have a task built by their different SP's, once they drop into Openreaches local data-base a 'wizard' will identify that there are 'Common faults' fed from the same DP/Cab and make one of the faults a 'Lead task'. The engineer then rings the 'Common Faults' helpdesk and acquires the info about the other faults which obviously adds weight to the faulting process that it could indeed be REIN.
What you and your neighbours should be aware of though is, if it isn't REIN and the circuit passes all the tests we have to do, the SP may well pass the charge onto yourselves. Again, by that I mean REIN could well be affecting your circuit, but if it isn't affecting Mr Smith down the road who feels he should help you by raising a fault, he may well be the recipient of a £160 bill.
I would carry on with your investigation work, I know there's an arguement there that says you shouldn't have to, but if you present your findings to your next Broadband engineer, it may well ease the process of getting the REIN engineers out. Like I've always said, I,we don't know for absolute sure it is REIN, thats why asking neighbours is always a good way of collating evidence, especially if you can nail it down to times with your neighbours when their DSL goes slow.