Bike runs great for 5 minutes, then sputters before eventually dying.

I have a 1981 Gpz 550. The bikes idles fine and rides fine for about five minutes. It starts with light sputter after that first five minutes of riding fine, then progressively gets worse until it dies out completely. 

Things I have tried:
-Initially I thought that maybe my carbs were clogging, so I cleaned the bowls and jets out with carb cleaner. I also measured the fuel level via clear tube method to make sure they were getting enough. 
-I tried running the bike with the gas cap open.
-I unscrewed the bowl drain screws to see if they were each getting fuel (they were)
-I measured the resistance of the two ignition coils. They both test around 2.7ohms. I have order two new ones anyhow from Z1 just in case.

There are two things that I am suspicious of but unsure if they would result in the symptoms my bike displays. First, the boots from my airbox to my carbs are a bit beat up. They are still soft, but two of they have tiny gauges in them from using a flat head screw driving to get they back on. They also do not have the retaining bands on them. I am not sure if a air leak from the air intake side of the carbs could cause this problem. Second, I just had to replace an exhaust manifold bolt, so while I was working in the head I re-shimmed a few of the valves to get to within tolerance. 

I have included a picture of one of the plugs in case it might help, it appears to be slightly wet. 

 So, I am wondering if you all have any advice. Thank you in advance.
 

You may be running too rich and fouling out the plugs.

Cover half of your airbox with tape.(this will cause a rich condition)
RIde it.
Better, worse, or the same?

Take off the tape and crack open your airbox.(this will cause a lean condition)
Ride it.
Better, worse, or the same?

Petcocks not flowing enough fuel? Try to run it with an auxilary tank of some sort. I use a bottle on an IV stand but you can get away with an old lawn mower tank held above the bike. 

Rule out fuel starvation by attaching clear tubes to the carburetor drains, When the bike starts sputtering, check fuel level.
However, the plug indicates rich. Turn mixture screws almost or all the way in. And/or go for a ride with the airbox cover removed.
 

Thank you for all the replies. Sorry for taking up your alls time. I am just an idiot lol. I did not perform a fuel level measurement correctly the first time and after rereading the procedure in the manual and redoing the measurement I found that 3 out of 4 of my carb bowls were holding too much fuel. Runs better now that they are all in spec. 

No worries. We have all done something similar. If someone else is having the same problem, then hopefully your thread will be of use to them.