I'm not meaning to be accusing or critical, but is it possible that maybe you only have some kind of vague image of what these other jobs mean? For example, you say you don't want to be a code monkey (which betrays your perspective on programming work). Certainly there are people who are practically 'code monkeys', but these are people who remain stagnant at entry or intermediate levels, don't do useful work, aren't curious and interested in applying their brains to difficult problems, etc. There is a huge amount that goes into writing high quality, reliable, and efficient software. It requires a lot of practical and logical thinking to figure out how to use proper data structures, how to architect your object hierarchy, how to make it efficient for future revisions and additions to the codebase, logistical issues like making it easiest for lots of people to contribute, etc.
I'm projecting a bit here, of course--I come from a programming background, but having studied physics for two years I'm moving back towards computer science, partly because of the dismal outlook for careers in theoretical physics (and the same can be said for pure math). Computer science, however, is practically applied math (though in a different sense, and with different math). If you enjoy topics like graph theory and general logic for things like building and optimizing networks, working on computer architecture, coming up with more efficient algorithms, applying statistics, probability, and linear algebra in conjunction with artificial intelligence (read: machine learning) to data mining/computer vision/robotics/etc., you'll be very happy with CS.
It took me a long time to get interested in things other than what I had plans for (which was theoretical physics). But the more you read about these other topics, the more you think about them, and the better image you have about the work, all of which of course contributes to building up a sort of passion for doing it. For me, I've realized that I like to solve difficult problems, and some of the most important problems today rely on making computers faster, more reliable, or more efficient.
Also, perhaps you can make the jump a little differently. Say, do a Msc. in mathematics concentrating on.... say, numerical linear algebra. Then go into CS and work in high performance algorithm implementation of your Msc. topics. "Going into" could mean do a Ph.D, or straight into industry. Or, say, you want to work for an aerospace company. So tailor your topic to work on numerical solutions of PDEs that are important in computational fluids research (it gets more specific, for example you can come up with a way to eliminate need for more artificial parameters so that simulations are more accurate and natural). I can't say this would be how you get hired by an aerospace company, but I know the basics of similar paths people have taken.
I'm saying all of this because of your comment earlier talking about when you're reading about cool mathematics, but wondering what the point is. Well it can be applied to lots of really awesome stuff, you just have to know where to look. As a person with lots of interests, I've spent a lot of time trying to figure out how to make the various jumps, from a physics student with heavy computational experience to actual hardcore computer science/engineering. It can be done, but most people don't do it this way which means you'll have to put your brains and social skills to the problem and forge a path on your own (and don't underestimate the social skills, some of the most valuable information I've gotten is from professors in CS departments who I've explained my situation to).