First an apology as my answer is not a how-to.
Going back some years I used to make much of my own equipment, but the cost of components and the difficulty of handling and soldering small modern surface-mount devices combined with the advent of global markets, where ready made equipment is often available for less money than the components would cost, has led me towards ready made units unless I want something special.
In the specific instance you are considering, the high frequency signals can make circuit layout important, possibly needing a number of prototypes and hence more time and cost.
So unless you have all the necessary equipment for PCB production and assembly and are really wanting to make your own for the sheer hell of it I would go for one of the ready-made solutions on the market.
These come in 2 flavours:
1) A transmitter and receiver pair that allow transmission of a HDMI signal point to point over twisted pair (cat5e or better) cable, these being the cheaper version.
They have different levels of performance, price not necessarily being an accurate indicator, some allow for remote infra red control some varieties, note that some require 2 cat5e cables for the link.
I have previously used these successfully over about 30 metres at 1080p.
I connected 4 monitors to a security system DVR, a 4 way HDMI splitter on its HDMI output, a direct HDMI cable for local monitor and 3 HDMI over cat 5e transmitter-receiver pairs for the remote monitors.
2) A true Ethernet solution that can pass over an existing data network, but bandwidth could be an issue and they are not cheap.
Many of these can transmit to multiple receivers, or more correctly multiple receivers can accept the signal from a single transmitter.