There are "connected devices" with the Sling App that do have ANALOG OUTPUTS. I know at least SOME of the WD line of products have analog output, but you'll have to go to the Sling website for the complete but VERY SHORT list of all the connected devices with the Sling App, and confirm they have analog outputs for your CRT TV, BUT . . .
the Neo and ALL the other "connected devices" ONLY work with the SLINGBOX product, NOT with HWS nor the adapters nor any Dish branded Sling solutions. The only way for you to receive Dish programming with the NeoTV (or the other "connected devices" such as the WD line and the OLD Boxee Box, and a Sony/Google product I can't recall) is to connect the OUTPUT of the Dish box via HDMI (HDMI may prevent channels using HDCP from passing through) or analog component (still HD) or composite video/audio into the SlingBox. The good news is that you can connect almost ANY device such as other cable or sat boxes, blu-ray players, TiVo's, DVD players, etc. to the SlingBox and Sling the content to your remote location.
The Sling App for connected devices and Sling App for mobile devices will NOT work with HWS nor Sling Adapter, which are Dish products. The Sling Apps work ONLY with the SlingBox products.
The cheaper WD Live seems to get rather poor reviews on Amazon, but the more expensive WD Hub gets far better reviews overall, and especially using the Sling App. I have both the WD Hub and a Slinbox 500, but I haven't had time to connect them. I going to invest in the Kindle Fire for my books and the Sling App for Kindly Fire, as well as Sling to my PC's. My content is on a TiVo, so the HWS and Adapter are not solutions for that content.