If you're a member of Mazda Motorsports Development (participate in one autocross or trackday every two years) then you can get an engine for about $3600 (MMD can't accept core returns so it's $2600 list + $1000 core) plus shipping. Many of the dealer will ship the engine directly to you. My friend got his delivered to IL from ProMazda in Houston. Delivery was $150 and return freight on his old engine was about $200.

The dealer I went through wouldn't ship but that's okay since it was only a 3 hour drive. I just pulled my old engine and took it with me. We swapped old for new and they did the core refund right there in person.