The transmitting power is probably higher than you think. The picture is noisy because the circuit is minimalistic, it's not operating in a low noise region, increased complexity (far beyond what you have) is the only solution and that means excessive cost and time to develop. You're FAR better off NOT trying to develop this any further as you'll end up with more wasted time and money in the long run over a commercial product that will perform as you want it to.
If there were truly a very simple high reliability high quality circuit that does what you want it to then we'd be using them already in our set-top boxes already. If you need quality use a commercial product, period.