[morzh]

What about the antenna tranformer not being plugged into the chassis? Would that solve the mystery with #7 burning?

By the Antenna transformer do you mean #3? (it is easier if you refer by position numbers).
No, that won't burn anything.

1. Here's the thing: all the tubes seem to connect through what essentially is a piece of wire (coils) for the DC current to the Plate voltage. So, yes, make the bias right and your resistor will smoke.
For this one to smoke quickly you will need probably several watts (don't know the rating), with 1 Watt being dissipated at about 70mA of current.

The problem is, you've disconnected the field coil. Without this coil there is (if we assume everything is intact, no shorts etc) NO power whatsoever to burn anything near #7.
This is why you can do whatever with your grids' biases - it won't hurt.

2. Now, if it smokes, there are probably shorts.
3. The single DC path to the RF 78 tube with the Field Coil disconnected is #55 resistor (32Kohms). If we are to assume it is intact, and IS 32Kohms, there is not enough current to burn anything, as it is about 10-12mA tops without any loads.
If however it is burned in the "low-resistance" mode, there may be more.
But: you have to have the tube IN the socket and it has to be shorted itself.
With the tube pulled out this path does not exist either.

4. You need to take your meter, disconnect the parts that smoke and start measuring, seeing where the voltage comes from.

Does it still smoke without RF 78 tube in place? WHat are the plate voltages? etc etc.

The usual approach to smoking situation is: follow the current path. Find the power source.

And, of course - be careful and safe.