What is the best method to transmit a DVI-D video signal from a FPGA?
I recommend you to use the Analog device IC ADV7511 cheap and best approach, which is capable of converting parallel digital pixel 24 bit RGB data from FPGA (LVCMOS) to RGB TMDS serial lines. But all the 24 bit lines should be length matched with respect to Clock, hsync and vsync in order to avoid skew.
Also do you have any requirement on output resolution. If output resolution requires 4K this is not suitable. This IC will support only up to 2k.
Reference schematics already available for this in Xilinx Kintex-7 (KC705), ZC706 based development kit.
Hope this helps.