you are using the Automake builtin support for tests.  It's 
quite
limited, and I believe it cannot do what you want.

>For example, I have to have a shell script to run 
tst_parallel below,
> because it needs to be called with the poe command, and 
some env vars
> set. In other cases, I need to call test program with 
some command
> line options.

If you don't want to stick with this, there are alternative 
testing
frameworks:  Autoconf's Autotest -- see the Autoconf 
documentation
(since it's a bit underdocumented and declared not yet as 
mature, it
may help to look at how other packages use it in order to 
get going).
Otherwise, there is always DejaGNU (big, complicated but 
can do a lot
of stuff).

I believe there are more testing frameworks, but cannot 
think of any
at the moment.  I personally use both the simple Automake 
TESTS for
easy stuff, and Autotest for some more involved stuff.