Mazda Financial would not allow me to buy out directly, stating that Florida leases must be purchased through a dealer.
I ended up using a company called Lease End. The process was smooth. My only complaint was that they required me to use their lender, which ended up being .5% higher than the credit union I was pre-approved with. Nonetheless, they were straightforward with set document and title fees, and did not try to tack on additional fees. I declined the extended warranty.
One additional point worth considering if you go with Lease End. If your lease is in Florida, it will require an updated title but it does not require new registration. I researched this on my own and informed Lease End of this nuance. This saved me an additional title fee. I think I worked my expenses down to the bare minimum possible.