If you want to run motors for multiple dishes, simply feed them from the different ports of a DiSEqC switch. Contrary to prevailing myths, DiSEqC switches and motors are designed to be compatible with one another and are intended to work in this configuration. There may be poor quality switches that cannot handle a motor load, but I've picked up ones for $3-5 that have no problems. I've also measured the instantaneous current from several motors under a variety of conditions and none exceeded DiSEqC limits.
It may be fun to dream about connecting Ethernet cables to a LNB, but this only demonstrates thinking in a very small box. The de facto design standards for FTA and DBS provide an IF bandwidth up to 1.1 GHz. With current technology one can easily route from an enormous number of LNBs through switches to an almost unlimited number of receivers with negligible losses in CNR. There are some products that can pass this through fibre instead of coax, but the concept is still the same.
GbE Ethernet bandwidth would be woefully inadequate to carry this as digital data, as one would need say 22X more than its peak (never obtainable) rate. One could put tuner(s) and possibly demod(s) in a LNB to accomplish what you want, but there would be even more problems with that, including the lack of scalability, vulnerability to technical improvements, power, reliability, cost, etc. While the current architecture may seem dated and is definitely mature, be assured there are very good reasons why it has not been supplanted.