Wow that's a tough one. Lemon balm outdoors is extremely easy to grow, to the point that it is becoming a weed in my yard. But indoors with poor light and poor drainage? Unless the wedding is coming up in a few days, I suggest you repot them in to small flower pots with drainage holes and then if you want the mason jars, just stick the flower pots in the jars. Then water can drain out of the pots into the bottom of the jar, but not be touching the soil.
Seems like a slightly odd choice. I like lemon balm and use it to make tea and jelly and in recipes. But I don't think it is an especially pretty plant and it is prone to getting the brown edges (like other mints). It won't be blooming and if it were the blooms aren't anything to write home about.
https://www.onlyfoods.net/wp-content/upl ... -plant.jpg
If you like herb plants, rosemary, lavender, sage or thyme would be prettier -- little starts in little pots.