Many people of commented on the difficulty of getting an accurate temperature measurement by simply attaching a thermocouple to the surface of the reactor. There is a better and far more accurate way to do it. That is a so called "thermocouple well" or "thermometer well" . The idea is to have an stub like indentation into the reactor into which the temperature measuring device is inserted. In ordinary chemical reactors it is not uncommon to have a well several inches long in order to get into the main flow or site of reaction. The wall of the well equilibrates with surrounding reactants thereby leading to an accurate measurement at the stub end of the well.
As for shielding, I have used more than 2" of lead to give a factor of ten protection from several MEV gamma. See the Physics Vade Mecum for tables of shielding requirements. For the specific case of a LENR reactor, I suggest that the reactor itself be surrounded by several inches of sand (silicon dioxide). The sand provides additional shielding. If sand is the only shielding, upwards of a foot or two of it will probably be required, with a much reduced amount of lead outside. It is probably experimentally convenient to provide an observation steel pipe through the sand with a steel or lead plug loosely fitting inside when not in use.
I don't know how the ecatX works, but I speculate that by providing two anodes (or cathodes) each connected to the ends of a split phase transformer that the system will self oscillate. It is often convenient to wind high frequency transformer with bifilar wire (two of them). Connect opposite ends of the two wires together and to the power supply, the two remaining ends are the split phase that go to each duplicated electrode. Electrical power can be extracted by winding a third winding over top the bifilar winding . Depending on the output voltage desired, it will probably be convenient for the third winding to be fewer in turns and heavier in wire cross section. Send that signal to a full bridge rectifier for output.
For safety, be very very careful about hydrogen leaks. It is notoriously difficult to contain. Chemical explosions with it are are common. Vent everything you can think of to the outside, including vacuum pump exhaust, over pressure valves, etc. A fan ventilating your lab is also a good idea. Watch out for switch sparks igniting a hydrogen-air explosion. Hydrogen is almost unique in that only a very low percentage in air is needed to cause an explosion (perhaps 2%) if my memory serves from long ago.
As for neutron shielding, boron is a classic. Borax from the washing powder department at the grocery store will do. Several boxes thickness would likely be required. This is a difficult calculation problem. Remember that neutrons are neutral and go through almost anything and then diffuse in air similarly to hydrogen. Thus the diffusivity is quite fast. Thus you need a neutron absorber on all sides. Neutrons can be all speeds and boron only absorbs a certain medium low speed range. Thus to do a really good job you need to add cadmium shielding to absorb the low velocity neutrons. Sand will do only a so so job of slowing fast neutrons down to boron and cadmium absorption ranges.