Michael,
I haven't looked at the schematic so I'm just talking off the top of my head here.
You speak of turning the H frequency coil slug in most of the way to effect a reduction in HOT current. Me thinks you have probably got the H oscillator way off frequency now and under these circumstances are also creating HF 'birdies' or unwanted oscillations, harmonics of which are able to sneak into and saturate the sound IF. Just a guess. Since you have no CRT on it you won't be aware of what H frequency you have unless you have measured it some other way than by synchronising to a broadcast picture.
Is there not an adjustable H. Drive coil on this set? That is what you need to adjust to bring the HOT current down.
Rob