Hi Bo,
My first guess is that you might be using standard DB25 cables where proprietary Tascam TDIF cables need to be. The pinout is different for TDIF than the analog DB25.
To answer the second question, YES, your 2408 can clock off of the TDIF input. Just select "Dig" as a clock source on the MOTU. I have the MK3, so I am only referring to that model of the 2408 when I say that your ADAT outs should be mimicking the TDIF inputs on every bank. Your setup should (will) work.
So, Are you getting a signal into the 2408 at all? If no, than check your cable type (proprietary TDIF cables Only), Check 2408's Clock source, (Dig) Also, you can go to your digital page (ALT/DIGITAL) and move the curser down to TDIF I/O and "DETAIL" to give you an idea of what is going on there. Does the Tx/Rx MODE say "Hi-SPEED"? That will work to your 2408, but not to your HD24.
You said that your routing is flawless out of the DM...All Good. How do you have your TDIFs routed? What is the clock speed you are using? If you are at a hi-speed clock rate on the DM, the TDIF and the 2408 will utilize SMux, halving all of your TDIF and ADAT output channels, but I think the HD24 is limited to 48Khz anyway, and the DM does not do sample rate conversions on the digital outputs.
Hope something in there helped.......S