Yes, after your experiments I guess it's now safe to say the Beomaster needs work.
IMHO it would be good to have the Beomaster serviced while it still works; there's always a slight chance of more damage if one of the filter caps dies completely.
It doesn't necessarily need a full recap, just the small electrolytics in the power supply and the 3-4 caps in the CPU module. It should be less than an hour of work for somebody who knows what he's doing.
It's curious that this mostly affects Beomaster 7000s, while the older 6500s usually still work OK. Perhaps B&O used better quality caps in the older series.