How many miles are on this tire and how is it defective?
If you are talking a hundred or so miles and there is clearly a defect, and you bought the tire through a bike shop and paid them to mount it, it should fall back on the bike shop to replace the tire for free and take it up with Avon. I know this may not be a great comparison, but if you buy a new TV and its dead out of the box or after a day or two, you would return it to the store, not contact the manufacturer.
Now if you have a thousand miles or so on this tire, that really blurs the lines. At that point if Avon admits the tire is clearly defective - not just the bike shop - then they should at least credit you a new tire. Either way, why is it so much out of pocket? Are Avons that expensive?
To me whatever gets you on the road fastest is best. At least up here the season is short, so I would rather eat $40 and have the bike for the two weeks.