Rather than attempting to guess the refresh rate beforehand, you could work it out at runtime, then use this to drive your main loop - something roughly like...(untested, obviously)

use Time::Hires;
$avg_num=10; # or whatever
$s=time();   #Time::Hires floating-point drop-in
$taxis->taxis() for (0..$avg_num);
$refresh = (time()-$s)/$avg_num;
$refresh = $sensible if ($refresh < $sensible;}

while(1) {
  $start=time();
  $taxis->taxis();
  do { 
     DoOneEvent( $running ? DONT_WAIT : ALL_EVENTS );
  }
  until (time()-$start > $refresh);
}
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Cheers, Ben.