[Arran]

If the high voltage winding is leaking to the electrostatic shield then that would cause your high current draw problem, very likely it's caused by rotted insulation on the power transformer leads. The electrostatic shield is normally grounded to the chassis so having 200 ohms between it and the center tap would make sense if the A.K has bias resistors in series with teh center tap and the chassis. You could probably fix it by slipping some heat shrink tubing over the respective leads, unless they are really crappy then replacement of the leads is probably the best alternative. I had to do this on a transplant power transformer and it's a bit tricky, the old wires need all of the tar and varnish cleaned off in order to solder to them, and the copper sanded thoroughly as well. Most larger power transformers, even new ones, have that electrostatic shield, but they use copper foil for that purpose and ground it to the lamination of the transformer, it's a way to eliminate power line noise.
Regards
Arran