Need verification on bad water pump

[Mustang Fanatic]

Hi, I own a 92 Mustang that I'm having problems with it overheating. I've flushed the cooling system and replaced the thermostat. The car will run high on the temp guage, right above the N in NORMAL on the street, but it will slowly progress to 270 once on the expressway (1-2 minutes hwy driving). After the last test run, I pulled the top radiator hose and no water poured from the hose. This was after running the engine for about 5 minutes with a water hose stuck down in the radiator so I know the block had water in it. Also, I pulled the serpentine belts and the water pump has roughly 1/16 to 3/32 of an inch of play in and out and up and down. It should be noted that when I was filling the radiator with the engine running I stopped just short of filling it completely and waited for the thermostat to open. I saw water stream from the cooling tubes in the radiator at one time today. I think the pump is in the process of going out and hasn't completely failed but I wanted a few more opinions before I replace it.