So, now this has turned into an agency bashing thread?
I have plenty of bad experiences with instructors from all major agencies. I have even more good experiences with other instructors from those same agencies. We all know that instructor selection is much more important than agency selection, so why are we smashing two different types of apples together? Are we making apple juice? I like apple juice...
OP, agency selection isn't overly important, however each one handles courses slightly different. For example, you're familiar with OW training through PADI. NAUI teaches how to recover an unconscious diver from depth. SDI teaches computers instead of tables. Slightly different approaches, but all teach you how to dive safely. That is, assuming you have a good instructor.
I know you mentioned plans to become a TDI diver in the future... The differences between agencies with technical diving is far greater than the differences between recreational. For example, max depth limits while breathing air is 130' for NAUI (Technical Decompression Diver), 165' for PADI (TEC50), and 180' for TDI (Extended Range Diver).
To hit that 150' you eluded to doing one day, you could take PADI's TEC40 and TEC45. Or you could take TDI's Intro To Tech, Advanced Nitrox, and Decompression Procedures. (AN/DP is commonly bundled together.) Or you could take NAUI's Intro to Tec, Technical Decompression Diver, and Helitrox Diver. (TDD/HD are commonly bundled together.) Three different agencies, three incredibly different approaches to technical diving, yet all teach you how to dive safely to 150'... PADI and TDI on air, NAUI on Helitrox.
Am I confusing you yet? Good! Your best bet to be able to do the dive mentioned in the original post is to seek out a technical dive instructor and ask them about the progression through their technical courses. Ask what and when something is learned, gear configuration requirements, whether computers, tables, or both will be used during the course, what decompression algorithm is used and why, etc. Then rinse and repeat with an instructor from a different agency. Keep doing it until you find an instructor that's right for you and an agency that best suits you. Have fun decompressing!