Update: I developed a work-around to get all the fonts to display correctly. First I changed all header fonts to Proxima Nova Condensed with a font-weight of 200px. Then I changed h2, h3, and h4 back to Proxima Nova with a font-weight of 600px using CSS. So far this has been the only way I've been able to get a thin Proxima Nova Condensed font to show up on Chrome, Firefox, and Safari.
If anyone knows a better way of doing this, I'm all ears!