DVLA cocked up and didn't change my licence address and made that very difficult.
A small but potentially very important detail - did you also update the address on the vehicle's V5C document? This is an entirely separate process to updating your licence, and changing one does not change the other.
I believe I did, but in that time period I also have several inquiries on-going with DVLA for other vehicles (purchasing and selling) many of which the V62's were lost on first submission and I believe that also happened with my personal vehicle when sending the V5C for this. I have various tracking numbers and receipts going to DVLA Swansea SA991BA
A bit of context about the inadequacy of DVLA:
For example, in early 2024 I had to complain to the DVLA executive that the CIO case worker unit did not process several V62's for purchasing of three vehicles from Auction. They lost the V62's from October 2023, I had to submit again in Decemer 2023, then complaint for about 3 months because they didn't look at the photo evidence sent to them via as requested and almost closed the V62 cases. DVLA executive apologised then stepped in, and still provided the log books late despite stating a date we would receive.
Someone internally in DVLA then went and looked up all of our company vehicles even going back to May 2023 and saw one vehicle which was untaxed but off the road and issued a fine for £300+, in a completely separate unrelated case to this. They also then issued fines for untaxed vehicles on all three of our new purchases stating they were untaxed in March 2024, in a malicious act. We received the logbooks in April 2024 and they issued untaxed vehicle fines for March 2024. The logbooks were issued by DVLA about 1-2 weeks before the April 2024 acc. They even couldn't adhere to the commitments made by the DVLA executive that stated which date out logbooks would be issued. We verified this by checking MOT status of the vehicle online which shows you when the last logbook was processed. So IF there were no postal issues, we had a two week time period to tax our untaxed new purchase or get fined. There is a stage 2 out of 3 complaint now with the DVLA for malicious retaliation and maladministration and misconduct.
(Note, we could not tax the vehicle, in the post office, online or via paper according to the CIO due to it being a casework investigation due to the value of the vehicles being high, which was my main gripe with them as we couldn't get the vehicles repaired and moving on.)
So that's a little background about DVLA being incompetent.