[Arran]

I've been cleaning chassis of late with a solution of TSP, about a tablespoon to a gallon of hot water. First, remove the dial, speaker, tubes, and anything else that might be in the way or get damaged. You then slather down the chassis with the solution, sometimes even poring it over it, let it sit for a few minutes, then scrub with a toothbrush, then you rise everything down with hot water and sit it someplace warm to dry for a week. I haven't tried it on a PC board but it removes filth from a steel chassis very nicely, plus has the added bonus of shining up the aluminum and copper.
With regards to what may be loading down the B+, I would check the tubes, there could be an intermittent short causing the problem. I would also take a look at some of the resistors and the pilot lamp socket, one of those may be acting up.
Happy Christmas
Happy New Year
Arran