Taking moonwave99's advice, I used DateInterval (can't remember why I went with DateTime for that in the first place, possibly a workaround for something at another stage of the project) and computed the seconds by adding each value to the total after converting it to seconds (converting hours and minutes to seconds and summing them up). I did this by using the DateInterval class's seconds property as well as the following function to convert a DateInterval to seconds (Note: only accounted for days, hours, minutes, and seconds for my specific case as there's no chance the amount will exceed one month):
function convertDateIntervalToSeconds($dateInterval)
{
$days = $dateInterval->d * 24 * 60 * 60;
$hours = $dateInterval->h * 60 * 60;
$minutes = $dateInterval->i * 60;
$seconds = $dateInterval->s;
return $hours + $minutes + $seconds;
}