Will I be able to enjoy the full experience at the latest seating time? I’d like to tour the kitchen and cellar, and possibly stay for dessert, but with the only reservation available at 11pm, I worry this won’t be possible.

It depends on the evening. We have to say an earlier time would be better.

Probably not.

It's unlikely you'll get the full experience at that time even if you do see the kitchen and cellar. I'd schedule earlier on another date if possible

Your best bet is to call them and ask directly with it being that late I'm not sure

Bern's at any time is worthwhile, schedule at a later date.