Many people still work from home for the DVLA.To try to hear back from a real person, I would send them a letter by first-class, signed-for, registered mail.I still put plates inside, but not like I used to.How about paying a month's worth of road tax by cheque "under protest" and asking for a photo?I don't think you were smoking it because you can't use Trade Plates for personal trips.
Have success with DVLA