Well, If you're using FCP, I have a trick to do it, but it's a pain in the ass to do for an entire movie.
You can do a hard text overlay. I don't know if there is a better way, but I've done it and it works, but I only needed it for a handful of lines, 15-20.
From the effects tab, under Video Generators, there is a folder 'Text' with several options, Crawl, Lower 3rd, Outline Text Scrolling, Text etc.. each one has different purposes, features and controls which will show up as a tab in your Viewer. To mimic subtitles I used Outline Text set to 24 pt. Worked really well. For positioning it's probably best to reset the x,y center, but I was lazy and just inserted 10 carriage returns and then did my lines and it lined up perfect. Once I made one successfully, I copied it and just kept pasting it over and over to save time in resetting everything. It creates a an overlay that becomes permanent when you export out of FCP.
This of course is a laborious process because it does not take advantage of your sub and srt files, and instead makes you enter it all manually with start and stop points, but it does work.
If no better route is suggested and you have to go this route, I'd recommend doing a google search for tutorials on how to use the generators, it's too late for me to remember which sites I used, but google gave me plenty of results once I found this section.
Good luck!