Moving in with my gf to the US - Both canadian citizens

I would be classified under the Computer systems Analyst category for the kind of jobs I am looking to apply to

Systems Analyst is one of the most heavily scrutinized categories, if you're going in as that you really must be one and the job title must be that or very close to it.

I suppose my ultimate question should be: Is there a legal way to be in the United States and be looking for work as Canadian citizen?

There are, but I don't think you fall into any of them from the sounds of it. You can legally enter to attend a pre-arranged job interview, i.e. pre-arranged from Canada, so you can look for work from here.

You can live in the US with your girlfriend while she is on TN-1 by being on B-2 as a "cohabiting partner" but basically what that means is that you remain a visitor indefinitely and you can't do anything more than a regular visitor who is there for the weekend. Even if you got married, you would be TD and you can't look for work in that category either.