hello Jennie, if you have some containers, you could still plant the small cloves and likely to harvest rounds which ought to yield good sized bulbs the following season. alternatively, if you're looking to store them for consumption, I'd crush/slice and dehydrate them or pickle in vinegar.
I'd be wary of planting between your asparagus unless you have lots of room between the plants, you might be surprised how far the asparagus roots extend - think of an octopus's (octopi?) tentaclesðÂÂÂ

This post was edited by zqnmegan on Thu, Oct 9, 14 at 19:26

Late November should not be too late. Here in zone 5 I've done garlic in mid November and it produced just fine.

Unless your asparagus is pretty young and spread out it would probably be better to find a different area.

Elephant garlic sprouts in my asparagus patch every year because I can't seem to get all the small cloves when I harvest it. The asparagus doesn't seem to mind so I think you have a good idea.
If you're in zone 8 you should have no problem waiting till the ferns die down in mid november to plant the garlic. It might not show itself as early as usual but should be up by new years.
As far as storing peeled cloves. If you want them for eating put them in a jar and cover with olive oil, then store in the fridge. Scoop them out as needed.

-Mark

I've found little or no change in size from October through December plantings in upstate NY as long as the ground is not frozen. They will set roots through the winter, even under the snow, and sprout up normally as long as they get through the freeze and thaw cycle.

Next year, I should have near 100lbs of Polish Hardnecks, the types that makes decent sized bulbs with only 2-6 cloves each. I've been purposely saving up more and more just because it makes for easier peel to focus on that species more. I also like it's spicy taste too.

Well i live in Zone 8 and the latest i've planted is in january, and my garlic has always turned out fine, garlic needs full sun, so i would recommend not planting them next to the asparagus. I have more info on garlic you can go here: Jubilee Produce