John Deer Z335e Runs Great for 20 Mins, Then Sputters and Dies

Hi all!
 
I've had this Z335e for about 3 or 4 years now, and it just started sputtering yesterday while mowing. At first it was very subtle, I could barely tell it was sputtering, then after 30-45 seconds it was more noticeable, and finally around a minute or so, it would just die.
 
I was able to start it right back up, and it ran good for about 10 minutes, then it did the same again. Started right back up, but only lasted about 5 minutes. Started back up, but died after about 2 mins, and this time, it would not start back up. Though after letting it sit for about 30 to 45 mins, it started back up and ran great for about 20 mins, then did the same thing again.
 
What I've checked:
The oil is topped off.
New gas.
I've loosened and also removed the gas cap with no difference.
I've cleaned the air filter.
I've removed the fuel filter, though not sure how to test it other than blowing through both ends, which was successful.
 
Does this sound like I need to clean or replace the carburetor, or the fuel lines?
I just find it odd that after it cools down or sits for 45+ mins, I can mow for another 20 maybe 30 minutes.
 
Any suggestions?
 

SRTsFZ6
Rule the fuel in or out.. Does the machine have a fuel pump??
 
If not, clamp a vise grip around the fuel line, right where it enters the carb. Remove the line from the carb, and with a suitable container, put the hose into the container and remove the grips. Fuel should flow easily and steady. Advise your results.
 
Also, have known good spark plug handy. When the machine dies, plug the spare plug into the wire and grind to the head. You should see plenty of spark. Again, advise results..

Thanks for the suggestions!
 
It does have a fuel pump, so any suggestions for testing this scenario?
I will also try the spark plug as soon as I get a chance.