List of Lenders that Allow Lease Buyouts without Dealer
Tax is unavoidable, if that is considered part of the $2700 in fees. However, I would ensure that the “Market Value Selling Price” listed is the same as your lease termination value (details about that calculation should be within the fine print of your leasing contract). Check the list I linked above and call the lender to see if they will allow for you to buy the car directly from them, as you may be able to avoid additional dealer fees.
I believe it is TFS that handles Mazda leases, and the list does indicate that they do allow for people to buy out their vehicle without a dealer.