Regarding alsa dmix, I don't know the technology,
but can
it solve the principle problem of two programs using
different sound servers? As I understand it, the programs
are using sound server API's and not ALSA API's so if two
sound server's can't coexist right, no fix in ALSA level
can help.
you can stack soundservers, but most often you'll not manage
to run them competively in parallel, except you use DMIX or
you have a special card which supports hardware mixing. Most
consumer cards do not support this.
Best regards
ce