Your assumption that I will be moving between 2 houses when I should be resting is once again, wrong.
I will be staying at an adress which is not stated on my NRIC
Then your question is wrong to begin with. What is on your NRIC is your registered address, but not necessarily your "home".
You are asked "Is it true that staff from army or MP will do checks to see if you are at home while on MC?".
So as long as you are staying at a place that can reasonably be considered a home, even if they check there's nothing wrong. You just need to let them know you are staying somewhere else and not out on the streets having fun.