Sounds like some kind of in rush current problem. I don't know anything about your amp but I'd guess it's something in the rectification (wrong tube type?) or voltage regulators.
You ever measure what's coming out of your wall socket just for curiosity sake? Mine gets as high as 125v certain times of the day..although that still shouldn't be an issue if everything is working correctly. I've seen people post numbers as high as 128v in older homes, which can eventually wreck havoc on older tube gear. Get you one of those Amprx Brown Box or their Linestage models from a place you can return it if it's no help. Works wonders on older tube gear and it seems like it cleans the power signal as well if compared to bypass mode. Cheaper options do exist. Although I think your issue is a problem in the circuitry if not the Rectifier. I'm no repairman though. Definitely not a power cord issue.