I don’t own an apple press, but I do have a juicer. Some of the juice I’ve got this year has come from big pressing days, using other peoples’ presses, but I’ve also made some using the juicer. It does work, but the juicer grumbles a little, so it’s best to do it in stages. I’ve also found that you get quite a lot of foam (think about when you get those posh fresh juices in cafes) on top of the juice from the way the juicer works, which it seems best to strain. You will also get quite a bit of juice from the pulp left over, which can either be re-juiced or strained into your fermenting vessel.
Not a strategy for any real volume, but doable on single demijohn scale. There is still hope for those who don’t own a press!