You can re-plant the shallots and you should get bigger ones next year. For shallots, you want to plant the small ones and eat the big ones (exactly the opposite of garlic) and give them some room - I usually plant shallots on 8 inch centers since they seem to want to grow sideways as well as up. They really like full sun in order to produce good sized bulbs, moderate amounts of fertilizer and decent water throughout the growing season.

I've done fall plantings with 4 inches of mulch and early spring plantings and I haven't seen much difference in yield so you might be able to plant this fall if the beds are ready.

Thank you so much! That was very helpful, and I'll try to get them in the ground sometime this week.