From an earlier post, might I repeat (forgive me):

Simply: if all the little ones and zeros are recognized properly by the receiving equipment in the proper order and are ‘captured’ within the ‘windows of time’ allotted, it matters not how pristine the actual electrical signals were or whether they arrived via gold, silver, copper, plastic, leather or horsehair. That is one of the basic reasons behind, and the concept/design of digital information, in the first place.

( http://ubb.outlawaudio.com/ubb/ultimatebb.php?/ubb/get_topic/f/6/t/000989/p/1.html#000022 )

Yes, there is a limit to a cable's length and still have viable functionality. In a quick online search, I found some practical HDMI-HDMI cables in the length you need for under $100. One needs materials and construction that perform, but nothing esoteric - only the information has to get there and be interpreted properly - the cable does not have to preserve the exact waveform and a certain amount of non-linear attenuation can be tolerated (horrors for analog signal delivery, but not for digital). And, since the projector likely has nothing to do with your audio reproduction, any DVI cables that currently work in your situation will also deliver HDMI outputs with an easy-on-the-budget adapter.