Option 2 is what I was trying to describe. mns stated it very well.
You should be able to assemble a movie that's just under three hours if you use Final Cut Pro, Premiere Pro, After Effects, etc. and then export that to mp4 (so, if your loop was 10 minutes, you would simply place that in your timeline 18 times).
If the TV displaying the title simply can't be there at any time, ever (even once every few hours - and I know it isn't ideal in any way), you'll have to find a TV that doen't do that via its own playback cababilities. There's probably a HD display designed for video wall use that will do this. Although, many of those models offer an optional Windows unit or dedicated VIDEO_TS playing unit for this type of thing (pricey add ons for an already expensive, yet usually beautiful display). If you find a consumer model that doesn't display the mp4 file name when the playback repeats, be sure to post it here.
I know you mentioned that there's no space for a DVD player or a computer, but have you considered a Mac mini attached to the back of the TV via a VESA mount adapter patched via HDMI? Secure and out of the way, it will really open up your options. I've used this setup with great results, especially now that recent Mac minis have HDMI out (sound goes via this port as well).