Well it seems unlikely the DVLA had been updated by the time the request was made.
That not withstanding if the DVLA had failed to update the details then the Police, despite using 'reasonable diligence' would have got the incorrect address so it still wouldn't provide a defence.
The S172 requests seem to have gone through a bit of chain implying previous keeper and dealership have been involved along the way, although as noted the dates seem a bit 'unusual', it looks like the entry on the 8th may have been a correction though not impossible a new S172 request was served.
The 6 month timeout is a long way off and I see no benefit delaying the response, regardless the S172 request MUST be replied to (details arrive with the Police) within 28 days of service, which is day ONE (not zero) of the 28. Service will have been presumed to be the 22nd of August (meaning a reply to them by 18th September but legally you have 28 days from the date of service (day it arrived through your letter box, not when you found it) so the 25th, although you don't really want to be defending an S172 charge based on date of service (though it's unlikely).
But really it would help to know speed/limit, if you would qualify a course it would probably be a bad idea to jeopardise that on a 'maybe' defence', a Fixed Penalty less clear cut, but if you are likely to end with a court 'summons' (Single Justice Procedure Notice) anyway then it may be worth exploring.