Yes, TSL is an age-related series. If you write to the DVLA's Fee-Paying Inquiries department, for £5 you can request a copy of all the vehicle's history as held by the DVLA (which will include details of former owners etc back to when the vehicle was first placed on the DVLA computer) As you've got an age-related plate, the DVLA ought to hold details of what its original number was, if that number was still present with the car at the time of the application for an age-related number.
BMU 460A means your original was almost certainly sold new by Two Strokes Ltd of Stanmore I'd say. If your original Bond has indeed been officially scrapped, then yes the number is gone forever. If however it (say) has been sitting in a field since 1968 (or whenever) then very likely the old card logbook was never added to the DVLA computer when the original DVLA log for such conversions closed in 1983. If you can find the car and its paperwork again, then you're still in with a chance. But as mentioned, if the car's been officially scrapped, then it's game over alas.
RegArchive isn't really worth the time of day. No matter what number you put in, it'll make out its got a hit when really all it's doing is inserting that inputted number into its automatic viewer thing. If suppose the number BMU 460A did turn up in a number plate dealer's stock, then yes you can get it transferred over onto TSL 128, provided the year quoted on TSL's V5 as declared date of manufacturer is 1963 or earlier. If it's declared as 1964, then again game over because "no number may be transferred which will make the recepticant vehicle appear younger than the date of manufacturer". TSL's V5 probably has "Non-transferable number" in the Special Notes section, but this only means you can't transfer that TSL number off onto anything else. It doesn't stop you transferring another number onto the car in place of TSL 138.
I'd like to find out where Dad's old Bond Mk G estate is now. That too was a Two Strokes car but hasn't been seen hide nor hair of since 1983. It's still "live" & out there somewhere though....