I may have found a way around this problem.

I noticed that the problem of the first notes playing only occurs
when the note is on beat 1, tick 0. Moving the note to tick 1 seems
to prevent it from playing. This has no effect on the metronome, it
still jumps to beat 1 ocasionally when paused waiting for midi.

Now you don't want to have to do this for every pattern, but there
is a way to move all notes back slightly for all songs.

In the play menu, under "Slide Tracks", set all the values to '1'
and select "Allow Any Slides".

I don't know if this will work for any and all styles. If it doesn't
work for some, possibly making the slide values a little larger may
help.

It even seems to work if the note is one tick before the 1st beat,
which is strange because "Slide Tracks" should move it back to tick 0
on beat 1.