Running hot and losing coolant: time for a new water pump?

Some short history: I've got an '01 TJ that I bought from the original owner. It's currently sitting at just over 300 thousand km on the odometer (approx 18,5000 miles)

At the tail end of the winter I noticed I was losing coolant. Inspected the radiatior and found it corroded and leaking. I picked a new one up, flushed the coolant system, and replaced the radiator. All the original hoses seemed good.

Now, the real issue: months later, the jeep starts running hot. Real hot. Like right up into the 125 C (260 F) range even on a very short "lets get this home so we can look at it" drive.

• There's plenty of coolant in the reservoir, but after 30-60 seconds after parking there's a thin stream of coolant leaking down from inside.
• It deposits a little less than half a can of beer's worth of coolant into the drip pan and quits.
• I've also gotten some slurping & sucking sounds coming from the radiator right after turning the engine off, along with a little bit of smoke (but I'm assuming if its running that hot, all kinds of old oil dribbles could be causing that)

Best I can see, it's coming from near waterpump, and from reading on here that would make some sense.

Does a failed waterpump seem plausible to you?

Or could I also be in trouble for failing to burp the system properly when I replaced the rad? I had zero coolant or temp issues for a few months with some long road-trips. Now this seems to have come out of left field.

I'm going to take a closer look today, and put the thermal camera on it (for all the good that's likely to do.) But I figured if there's any help to be gathered from the online jeep-hive mind I'd ask for it! Thanks guys.

Running hot and losing coolant: time for a new water pump?