The concept of a truly useful DIY laser TV is uncharted waters for the most part. The closest that has been done with good color distribution and decent picture quality is RGB raster imaging using a relatively normal RGB scanner setup, but the resoloution is nowhere near what most people would consider "television". This entire thread so far has been just speculation about the types of technologies and techniques to use in such a project. If you want tp build a DIY laser TV, then judging the practicality of such a project is up to you. What I can tell you is that short of some real ingenuity, the costs outweighs the outcome in most cases. The real ingenuity would come from the mind of whoever decided to undertake the project. If you were to invent some new methods of doing things, the project could suddenly become a much more realistic goal..
Regarding DLPs introducing speckle noise, personally I have no idea. Someone here may know more, but I doubt that many people on this forum have used lasers and DLPs together in their hobbyist projects..