After going through a handful of unsuccessful attempts at WordPress plugins to manage and link my downloads, I finally found one that worked: WordPress Download Monitor.
So I’ve completely retooled the Podcast page to where you can actually download the podcasts manually from there. I tested all of them already. They work. PC users, please, please, please right-click and save so as to not kill my bandwidth. Mac users, do whatever it is you do to save files. I don’t think it’s right-clicking, but I wouldn’t know as I don’t own an Apple computer.
That is all!