Hi Hilary!
Date night sounds great and there are so many fabulous places at Epcot for drinks. I completely understand your need for non-alcoholic versions right now but not to worry, you'll find plenty of those too.
If you have a later dinner reservation, you won't be rushed to finish your meal. However, the places that do offer a more true bar setting like La Cava typically stop serving near the start of IllumiNations so I wouldn't plan on a late night there.
Since you'll be in the area, you could go from Epcot over to the BroadWalk to
Jellyrolls. Its a dueling piano bar and its great fun.
If you're looking for places that stay open later than the bars and restaurants in Epcot, you could try one of the lounges at one of the Resorts. The Wave Lounge at the Contemporary Resort would be convenient for you as would the California Grill Lounge (if its reopened by your visit).
Another option is Downtown Disney. Many restaurants offer full service bars. If you're looking for something a little more quiet, try Fulton's Crab House. They have a nice bar area that sometimes features live music on their deck. Portobello also has a nice atmosphere at their bar.
If you're looking for a more lively atmosphere, try Bongos Cuban Cafe, Paradiso 37 or Raglan Road Irish Pub and Restaurant. You can often find live entertainment in these places. You don't need reservations to sit in any of the bar areas but if you'd like to plan on a having a meal in the restaurant, you can
make reservations online or by calling 407-WDW-DINE.
Thanks so much for visiting me again!
Wishing you minnie magical memories :-) Allison V.