I do agree too that plain hot alumina still can't be really defined as a conductor and that this shouldn't be normally happening. After attempting a few calculations some time back and realizing that, I actually even told Alan Goldwater that something else besides the volume resistivity of alumina decreasing by a few orders of magnitude with temperature should have been involved.
My hypothesis is that the process of heating at high temperature the alumina/ceramic tube in these replications with nickel and LiAlH4 can under certain circumstances deeply alter its electrical conductivity properties in a way that short circuiting paths to the resistor wire could form over time. I don't think that the entire (or at least the portion affected by Ni-LiAlH4) tube is becoming a conductor, but I can't exclude this possibility.
I'm not suggesting that milliamps will be enough to trigger observable LENR, but rather that this effect seems large enough that a clever and deceitful person such as Rossi could have planned things out in a way that at a high temperature and sufficiently high voltage a substantial amount of power might be directly discharging into the nickel powder by design, and that this could have accidentally happened to some of the successful replicators.
You are definitely right, that the electrical resistance of alumina will decrease with increasing temperature. Good hint.
However I would not suggest to bring electrodes into contact with the tube in order to apply an additional current.
If me wants to continue to use a current source (fixed current, variable voltage) this means that at the points where there is higher resistance, joule power will be larger thus we will induce thermomechanical stress at these points. temperature differences should be as small as possible in order to prevent cracks at the tube surface.
You could try to place swageloks at opposite sites of the tube and apply the electrode wires there.
However, I think the transformer that me mentioned is the much better solution. You can generate strong magnetic fields with MHz to GHz frequencies and induce vortex current inside the tube. Without any contact between trafo and reactor tube.