As been stated ( and initially suspected ) the cable pair your service is on is from a DP that is served directly from the exchange (E/O ) , and for whatever reason your neighbours service isn’t from the same DP as you , but a different DP that is via a PCP ( cabinet ) hence their access to FTTC,
realistically there isn’t any chance that Openreach will rearrange the existing copper network in your area ( possibly at a considerable cost ) to give you a relatively small increase in speed, their emphasis is on the FTTP rollout , copper pair rearrangement is not a priority, TBH , even before the focus on FTTP , this sort of scheme ( copper pair rearrangement ) was rare if the costs massively outweigh the benefits .
As far as the variation on the records , in your case it’s the phone number is returning the incorrect information and the postcode the correct data , at best the Mods intervention will align the phone number return with the postcode , and as previously stated once you are migrated to DV ( the fact you are on ADSL2 probably the reason why you haven’t already been moved ) the phone number option on the DSL checker doesn’t work anyway .
