You expect them to hand you a new strap for one that has been used for a week?
You mentioned that they have invited you to many events and dinners etc. and that in itself is exemplary public relations and customer service. You have been treated as a VIP!
As for service in the boutique, they set standards that others wouldn't even come close to emulating IMO.
I agree with their principle, it's not a matter of the cost for 1 strap. They will gladly give you one or two if you have purchased watches from them directly or even a deployant for a higher end piece I believe.
Don't take this badly but you are expecting too much and I don't think any retailer is able to do the sort of exchange you are demanding. Something worn can never go back on the shelves again.
The best solution for you is to sell this like new strap and get yourself another one.
cheers
fernando
"And it really should not matter where I bought it"
I totally disagree with the above. It's imperative, let me stress EXTREMELY impertative, in this situation.
Since you wrote the above, I am assuming that you did not buy your Langes from this particular Lange Boutique. And just because you are a customer of the BRAND, you are NOT a customer of the BOUTIQUE.
Customer service, in my opinion, goes to where you purchase your watches. So if you did buy your Langes from this Boutique, I would expect them to show you good customer service and offer you a free strap because you ARE a customer of the store.
You cannot expect good customer service from any establishment where you have not established a relationship with them. If you haven't bought anything from a store, do you really expect to them to bend over heels for you? Absolutely not.
If I'm a customer of Ferrari and bought 100 Ferrari's from other authorized dealers and secondary dealers and also through auctions but I didn't buy any car or anything else from Store A - and then I go into Store A and tell him "Hey, I was here last week and bought these rimms from you but I changed my mind. I know these rimms are used but I want those other rimms right there instead." What do you think Store A will tell you?
My 2 cents,
Anthony
"And it really should not matter where I bought it"
I totally disagree with the above. It's imperative, let me stress EXTREMELY impertative, in this situation.
I 100% agree with this post. The fact of the matter is that a boutique is probably the most expensive option to purchase a watch--i'd imagine an authorized dealer would be more willing to discount. That being said, what you get for spending that extra cash presumably is better service, i.e. getting a free strap thrown in in the correct size (my view of the original issue. i don't see any place accepting it for an exchange) or the first look on a limited exchange piece. Maybe an invite to some of the marketing stuff that lange does (which to my knowledge is generally set up by the retailer vs. the manufacturer itself).
If you had purchased from the boutique, i would have been surprised that they wouldn't throw in that strap (if not both) for free. But for just owning a lange...with all due respect i think your expectations might have been a bit excessive. I'm speaking as a US customer and I'm fairly certain that would hold here as well as asia or wherever else.

1/ You are a client of the Boutique, where you bought one or several watches from them, then they could / should have done something for you.
2/ You are NOT a client of their Boutique, and I can understand why they don't won't to change your used / worn strap.
I can also understand that you will not do any business with them, either!
Best,
Nicolas