Apologies for saying what some others have said, just in a different format. My comments inline:
As a DM trainee, you may not be given a whole lot of real diving tasks. Helping out in a pool or otherwise holding the hands of student divers won't push your skills envelope toward your stated goal of technical diving. Instead of using a DM course as a way to get in more diving, I would recommend finding some buddies and using your limited time and money to do more "real" dives.
Become a better diver-better buoyancy, SAC rate, skill confidence
You would learn these skills better by, in addition to just diving as noted above, taking some specific courses. I don't know about NAUI, but I know PADI has the Peak Performance Buoyancy course. Perhaps better yet, and although not well publicized or widely available, you may be able to find something like a "scuba boot camp" offered by an instructor on an individual basis. Or, after getting in some "real" dives as mentioned above, you might be able to use Intro to Tech as a course to further hone your buoyancy, trim, propulsion and related skills (whether an instructor views ITT as a remedial course or expects your skills to already be very good may depend on the instructor's individual philosophy). GUE's Fundamentals course would fit your needs but is even more expensive.
Become a better buddy-rescue, O2/First Aid, self-sufficiency
Take the Rescue course or whatever NAUI or other agency calls it. I doubt that a dive shop will take you on as a DM trainee if you have not even gotten that far on the ladder of courses. If a shop offers to give you other courses "for free" as part of a long-term internship program, they're going to expect you to work--probably harder than you would have at Wally World.
Prerequisites for the diving I want to do- Esst. of Tech/ANDP
To reiterate, my advice would be to just take the courses that teach those prerequisites, and do a lot of quality diving between courses. The skills you learn as as a DM do not translate perfectly to the skills you need as a technical diver. I am not an instructor, but I have heard tales of experienced DMs and even OW instructors having to re-learn lots of skills when they decided to get into tech diving. Really, they could be considered two quite different paths in diving.
Cost is a HUGE con for the path I propose above. However, if you consider how much money you might spend being a DM and perhaps not becoming as skilled a diver as you could have, it might not be that great a difference.
Regardless of what path you take, if you don't put in the time you will not be the kind of diver your are describing as your goal. Maybe the best solution is to wait until you have more time and money and, in the meantime, just do as much decent diving as your time and money allow. When I was in my 20s I would have loved to have gotten as deep into diving as I am now, but I didn't have the time or money.