From past experience with AC heater coils, it is possible to generate a large common mode AC signal on the thermocouple by coupling through the capacitance between the coil and the thermocouple; and, in this case, to the nickel container. This can be mitigated to some extent by using 100 ohm resistors from each of the thermocouple connections to ground and use of differential measurement of the thermocouple.
However, in this case, I don't think that is the source of the rapid fluctuations. Below 200C and above about 900C, the measurements smooth out even though above 900C the voltage driving the heater coil is highest and would produce the highest coupled common mode signal. The fluctuations are most noticeable around 280C and between 600C and 800C. Around 280C the first breakdown of the LAH occurs and between 600C and 800C another melting phase occurs. When these phase changes occur, H2 is released and the LAH foams and sputters. It is likely that as the LAH foams and sputters, hot spots come and go on the tube. Since only one spot is being measured, I think you are seeing the result of the LAH foaming/sputtering inside the tube.
To eliminate the rapid variation, the best solution I can think of is to use a more distributed temperature sensing or multiple thermocouples along the length of the fuel tube averaged together. One way to do the distributed sensing would be to wrap the length of the tube with an insulated wire (a little problematic at these temperatures) and measure the resistance as a function of temperature (a large coiled RTD).