It will work with your 44 switch, but you would not need it. The switch is built into the lnb on the 1K4.
You can buy the dish & install yourself. You will also need to call Dish after you install it & have ran a check switch. They will need to do an arc change over the phone for you. Be prepared when you call & state facts & that you are changing because of LOS issues. As an installer we do it all the time, but have not heard personally of non installers doing it. Good luck, I'm sure you will get something figured out.
Actually there is no need to call E* if you already have an activated receiver and install your own dish.
Why not just sign up for DHPP and get a $30 service call to verify that LOS is actually the problem. Drop DHPP afterward. It also may be cheaper for E* to put up a new antenna for you than for you to do it yourself. They've been charging $59 and in some cases nothing. They will usually do it for free if you agree to a 24 month commitment for service.