Honestly I did your first option (a pull-up door roughly 16x12) but after opening and closing manually with a rope and pulley system I ended up buying a cheap motor on Amazon and made my own automatic door. Had the coop power plugged into an old-school lamp timer (like the one your parents thought would fool potential burglars when you went on vacation, now - dirt cheap) and that would open the door at 7 and close at 9p.

Add-A-Motor - Chicken Coop Automatic Door Accessory Motor - Model D20 - 120V https://www.amazon.com/dp/B007IZJWNQ/ref=cm_sw_r_cp_api_i_BVZF7CD0SM4K0R0TET3B

20 dollars more expensive than normal for inflation I see. But mount it maybe 6-12 inches above wherever your door lies in the highest position. Use the supplied string to attach to an eye hook at the top of the door. Keep the slides and door on the interior of the coop. And put stops in at the base. Make sure your door is heavy enough that a raccoon won’t be able to lift it.

And viola. Automatic door. I’ll look and see if I have any old pictures of the setup. But cheap and easy.

Add-A-Motor Chicken Coop Automatic Motor (D20) https://www.amazon.com/dp/B007IZJWNQ/ref=cm_sw_r_cp_api_GPelAbFTK237R

I have used one of these for about 4 years now. I used a piece of scrap plexiglass for the door because it won’t warp or swell. It goes in a track made from 1”x4”s. It is important to use the little cotter pin quick release in case it gets stuck or it’ll strip the gears. It works great and is very convenient.