You could probably do it with an m3u8 playlist by just repeating the same segment(s) over and over again (maybe with #EXT-X-DISCONTINUITY tags in there when it repeats). It's a bit of a hack. You could make it a little cleaner by having your server simulate a live stream using the same idea.
I just tried it with a 2 second segment and it seemed to work:
#EXTM3U
#EXT-X-VERSION:2
#EXT-X-TARGETDURATION:10
#EXT-X-MEDIA-SEQUENCE:1
#EXTINF:2,
seg0001.ts
#EXT-X-DISCONTINUITY
#EXTINF:2,
seg0001.ts
#EXT-X-DISCONTINUITY
#EXTINF:2,
seg0001.ts
#EXT-X-DISCONTINUITY
#EXTINF:2,
seg0001.ts
#EXT-X-DISCONTINUITY
#EXTINF:2,
seg0001.ts
#EXT-X-DISCONTINUITY
#EXTINF:2,
seg0001.ts
#EXT-X-ENDLIST