It's very disappointing to hear that Sharp is unable to supply you with a set. It's understandable that, at first glance, the sets at retailers are irrelavent becaue they no longer belong to Sharp. But, if the decision has been made to replace your set and now two months have passed without a replacement there may be a question of the warranty company making a reasonable attempt. I just purchased my warranty through Sharp ( I assume you have this warranty also) so I don't know the specific language, but there will have to be language that addresses the effort that Sharp must go through to fulfill the contract.
While Sharp , through it's warranty company, may have had no need to consider going outside it's own internal suppy chain to replace your set initially, now, two months later, the question of reasonable expectations of the contract fulfillment should be raised. When they advertise a 24 hour/7day a week service / replacement in their policy, I think waiting 2 months for replacement of a set that is in current production is unreasonable. The secondary option of authorizing an outside purchase is a choice they have to consider if they cannot come up with a TV set. I truly believe the statement that they cannot come up with a set is not accurate and you need to push that. While Christmas has probably pushed a lot of inventory out to the retailers, I cannot believe Sharp, in its entire inventory, cannot find your set. I would start/continue dealing with Sharp directly, start playing hardball with the warranty company, contact your local consumer protection agency and see if your local TV station has a consumer advocate reporter.
Be firm, be courteous, get names, write everything down, don't give up and good luck.