This probably isn't going to be helpful, but back in the early '80s I scored a free OS3300 from the Calibration dept as BER (apart from rubbed front panel markings, they possibly couldn't get a spare transformer or tripler even back then). The 3300 is the same as the 3000 but slightly higher bandwidth and a potted EHT trippler. It was suffering the same problem as yours, overheating and failing BFY50s but otherwise working.
Being very green in those days, I replaced them a couple of times and then fitted a couple of uprated TO126 package BD-something-or-other, heatsinking them to the EHT unit box, like TR813. It ran for a few weeks like that and then, when I had the lid off, I noticed that the EHT box was running cool and remained that way for many years, until I passed it on.
I've often wondered what the cause was, I think I rationalized it as a failed capacitor in the potted tripler self healing but I was never sure. Nothing quite rang true, there was no apparent drop in EHT or CRT cathode bias, focus etc. Likewise the transformer, a shorted turn would probably have caused more severe symptoms. So I'm really not sure in hindsight.
I'm not suggesting that you do the same thing without further diagnostics, but it doesn't appear to be an isolated problem. I think they do run the BFY50s a bit too hard. A shorted TR814 or 815 would almost certainly take out TR813 as collateral damage.
As coromonadalix says, be very careful with the focus supply (B) as it provides the feedback that the EHT unit uses for voltage regulation, causing it to overload, as would an open circuit EHT adjust pot or connection. It would be worth checking the track resistance of the focus pot too.