All I was saying, is a heater core that has clean HOAT coolant flowing through it at all times, doesn't clog itself.
I understand the time part of the dash, was simply trying to say it's not too intimidating once you've got into it. Hardest part is dropping the column and it's actually not bad either. I usually draw a mark around the mounting nuts for it so you know it's exactly where it was. Also a good time to regrease your steering shafts and joints.
I may not have done my dash myself, but I have on many cars, as well as my friends 04. Usually the processes (and even mounting points) are relatively similar. Only difference with jeeps is they come apart easier IMO. All tends to weight less and be more compact as well. As you've already noticed with the glove box (checking the blend door whether its being actuated) and how easy it is to remove.
Was simply trying to let you know it's doable. Especially with info found in the searches on this site (just no definite how-to).
The water pump, if youd rather do first, there is a definite how-to as well as many threads and info on. Quick and easy, and you can you a reman from Napa that plenty have had success with but I went Mopar.
Thermostat, definitely Mopar.
I had shifty heat with my last water pump pretty bad, would only work when I was driving and would get hotter as I accelerated. When I came to a stop I had to turn it off or feel the temperature of outside blowing at me at whatever selection I was on(in winter it would turn to basically AC temp in your face at a red light).
Now I've never bothered using my infrared digital thermometer to check the temperatures of the heater hoses, nor vent temperature so that's the only reason I didn't try to relate to that info.
This was all just just personal relative information. As well as an attempt to save you money and hopefully grief.
My professional opinion would be, if it seems like 1400 would be easier to pay for it, then do that. At least then they can be there in person to run the necessary diagnostics themselves and confirm the issue beforehand.
Btw when my heat was bad enough to be that cold at a stop.. it was to hot to directly point at you at highway speeds.