there isn't enough depth behind that fitting to insert a sender, if you want to do something like that you need to use the same location your regular gauge sender is installed [which should already be a mechanical one], but as suggested a good laser digital termometer will do the job to determine if the gauge is accurate
with everything new as you list, I'd suspect the gauge or an air lock at the thermostat, did you drill the small hole on the thermostat flange as usually suggested?
Bill