I do this with folks PST, so minus 3.

A lot depends on your org. I work a regular day east. Last time and if a meeting comes up after hours I do my best to attend. If I can't, they understand. Takes some juggling though. I find my hours tend to end at 6 more frequently so I take it easy in the morning. I'm also an early riser but I don't think they'd go for a gig where I'm basically working 4am to noon their time.

It will depend a lot on the people you work with. You need to be accessible to them throughout the work day, you'll need to make their work hours your work hours. If they're willing to work with you on an alternative schedule, it might be that you can work your hours earlier in the day, but need to be checking email and available by phone throughout the rest of their work day in case something comes up. Your need to talk to your prospective employer about this, we can't tell you what they'll say.

I'm considering a position on mountain time, so two hours behind us. I also have a little one I'd like to spend as much time as possible with. I'm also an early riser. How do people who work remote schedule their 8 hours if the company is in a different time zone?