If you are using Premiere 15.0 it should be pretty easy to change the caption stream to Open Captions or Subtitles. You can make creative adjustments to them if you need, and they should be burned into the video. Worth a shot.
This should work in the new PR 2021 and older. And it should work with 708 or any caption format. I just tested in 2021 (exporting to h264), and it worked. I am Win10.
However, there have been earlier releases with bugs where captions did not burn in correctly. And some users working with PR 2021 who are having issues. Because of all the differences form earlier releases, it remains to be seen whether these are bugs or a learning curve.
So what version are you working in? Windows or Mac?