We worked on ovens back in the day when the average one was more expensive than now, so this is where I saw this happen. The easiest thing to detect leakage you could use is a CRT display old computer monitor or cheap tube tv . Put the set running near the set and if the microwave is leaking the set would react like running a magnet over the screen. Set a short run time on oven if nervous about running. Not an absolute but it might give you an idea. Should not hurt the CRT if you are worried, the set may need to be degaussed if anything. CRTs should degauss them self at start up next time its powered off for a short period of time. If the TV set is too far away it may not pickup, but you shouldnt have to hold it right up to the door. Might need the display showing something rather than black to see it best. CRT monitors might turn off display if no signal detected, TV would have a blue screen or snowy raster might be best. Microwave leakage meter would obviously be best way to check this though.
Trying to test it with other devices phone, laptop is they just dont operate on near the power of the oven. The perforations on door might be cut more for 2.4ghz range which would be why a wifi laptop would be more affected than your phone which runs on a different frequency. The door is likely to heavily attenuate any rf signal regardless though. Could leak elsewhere but seems unlikely.
You never mentioned what type of cable comes from the receiver to the TV. If HDMI try component or vise versa. Does the TV messup with same input but different device? If you pull up a full screen menu on the DVR does it interfere with menu too? If you disconnect the satellite cable does it still messup? Just trying to see where/what the microwave is interfering. Is other microwave running on same breaker as hood one? Is it same wattage? Maybe this could end up being an electrical wiring issue only noticed by the heavy load of the oven running.