If you get a message about "m_state" ........ and a bunch of text that is not really all that useful then I would start suspecting that reset could be an issue. If the download just says that the validation failed then it could be any number of things including a memory problem.
The SDR SDRAM controller doesn't make use of the first 0x20 words in the memory for calibration so you don't have to worry about that. I would recommend using a non-volatile memory for the reset vector since that's what the processor starts fetching instructions when coming out of reset.
Your code probably wouldn't be located anywhere but the first ~80kB of the memory however the heap is probably located in the memory you are testing so I wouldn't recommend doing that. You could hack the memtest software to allocate the memory instead of having it ask you over the terminal. This way it'll be safe for the test to clobber it since it was either allocated at compile time or at run time.