I actually tried a couple of different .srt files for the same film, and got the same problem for both. I then tried the same .srt with a DVD version of the film, and it worked fine. I then tried this program tsMuxer to create a new file with the srt file, incorporating the appropriate delay. This appeared to work at the beginning, but apparently there's a slight difference in speeds between the DVD and bluray versions, because it went out of sync later on. Playing the DVD and bluray versions side by side, I confirmed that the bluray version was playing at a slightly different speed. So the problem remains.
Thanks for the jubler link -- I saw it after I watched the (DVD) version of the film, so I'll try it next time I have this problem. Would love to know how to fix it if only out of curiosity.