NP-hardness proof: looking for some good restricted np-hard problems
I don't know if there is a machinery way to do this, but my little personal experience works as follows.

I try to provide a polynomial time algorithm for a problem. In those tries usually I can see there are some restricted versions of problem which are polynomial time solvable. I also will understand what part of my algorithm was handwaving for original problem. I can compare this two cases (difference between restricted versions and the general one also the part of an algorithm which was hard to improve). By comparing those two cases usually it's possible to guess how does the problem bottleneck looks like. So we can find a related hard problem. Usually providing an algorithm for a problem is hard job, and needs good knowledge about a problem. After we get this knowledge about the problem we can have many different ideas to tackle problem in different scenarios (not just hardness results).

P.S: If your proof relays on a particular problem, I think it's because that problem is very close to your work, so don't blame yourself.