I have a few characters on EU that I made to play with a group of friends, but they left and our group play never really materialized. For that reason, I want to move 'em to US servers. In addition to doing that, I should also end up missing only one class for legendary status

I'm quite familiar with that feel. Feel better soon!

At the bottom of the minimap, you'll see something that says "PVP" or "PVE". If you right-click it, you can toggle between the two instance types.

At the time this thread was posted, Summer Time had ended in Europe (it usually ends about a week before it ends stateside). Because of that, your time conversion site gave you a false report. The times as posted in the opening thread are correct. 1am PST is 9am GMT. It's also 7pm AEST, if I've done my math correctly for those in Australia.