I haven't found a way of exporting soft-subtitles yet, but it's relatively easy to burn hard subtitles to .mp4 files using shareware (on a Mac). First Control-click on the .eyetv file and select Show Package Contents. Then drag the .mpg file into MKVToolNix, select all boxes, including the DVBSUB file, and then click Start Multiplexing. This takes less than a minute to output an .mkv file. Next drag this .mkv file into MP4tools, select all boxes in the upper part of the window and then, in the lower part, select H264 (either 1 pass or 2 pass) under Video; select Pass Thru and AAC (2-Ch) under Audio - plus the kbps rate you prefer (I typically select 320); and finally select Burn (hard) under Subtitles (Mux-soft doesn't work for DVBSUBs ). Clicking send will then output an .mp4 file with burned-in subtitles. Be patient, though, as this can take a long time, especially if H 264 (2-pass) is chosen.
Alternatively, the process is simpler if one purchases MacX iPhone Video Converter. Just drag the .mpg file from Package Contents into the window, select .mp4 in the pop-up box and then simply click on Disabled Subtitle and select Track 1 (English). When this is run, an .mp4 file with burned-in subtitles is produced, though again it can take a considerable time.
Bon chance!