You can use a regular BP Protege trans, easily found at a junkyard and the MazdaSpeed LSD from the MazdaSpeed Protege can be adapted to work in that transmission.
As far as which one is faster, the BPT can be made faster pretty easily just swapping turbos and upping the boost. The KL-ZE is NA and you won't get much more out of it than the 200hp at the crank it normally makes unless you turbo or supercharge it, both are expensive and a nightmare to do because of the amount of space the KL takes up in the engine bay.
Easier to get parts? Both about the same. Many parts of the KL-ZE are found in the regular KL-DE, and many parts of the BPT are found in the BP-05.