1978 KZ650 running issues

Currently working on a 1978 KZ650 that hasn't been running for many many years....so far to get it running, I gapped the contact points, and made sure the timing was correct, rebuilt the carburetor by cleaning it and putting all new jets and gaskets into it. I then bench sync'd the carb, adjusted the float bowls, and adjusted the pilot screw 2 turns out from "lightly seated".The issue I am having is: When I start the bike up with the choke on the bike will start up but then it begins to sputter and eventually dies. when I start the bike up with the choke lowered and raise the choke the bikes RPM's increase. Whenever I turn the throttle the bike will die. I checked the headers to see if they were warm. Headers 1 and 2 were warm while headers 3 and 4 were hot.Side note: Occasionally the bike will start up and continue to run for a few minutes while the RPMs remain in the 500 - 1000 range.
 

Welcome.
All four exhaust pipes should get equally hot.
Maybe 1 & 2 are not firing well.
Bad spark plugs?
1 & 2 don't share the same coils; 1&4 share a coil, as do 2&3.

What size jets did you use, and are you using a stock air box and air filter?

Fuel level should be checked with a fuel level tool (tube) with gas in the carbs.
This can be done with the carbs off the bike and level, or with the carbs on the bike.

Different carbs, but the same procedure.

This level is too low, should be up near the top of the bowl:

The first thing to do is determine if it is fuel or spark related, then go from there. 
You say you cleaned the carbs but, in my experience, there is a difference between cleaning the carbs and CLEANING them. A search will provide you with a detailed how to-on making sure the carbs are working as they should. 

This link my help you to determine if the issue is intake or electrical      www.motorcycleproject.com/text/the_60-40_rule.html  

What specifically did you do when you rebuilt the carbs?  Did you ungang the carbs and soak the bodies in carb dip to clean the inner passages?  

Spark plugs are brand new, Spark plug caps are brand new, Ignition coils are brand new (installed them today). I was surprised that the #1 and #2 headers weren't warm while #3 and #4 were scalding due to the timing looking good. I setup the floats to allow enough fuel to be approximately 1/8" from the top using that exact float bowl tool. Carburetor has all stock jets (I have extra parts if i need to change that). I actually was running the bike without an airfilter. I have the filterbox but it isn't currently attached since it need new grommets for it. I plan to get some K&N pod filters.

I replaced all the brass carburetor parts with new parts and sprayed all the passage ways in the carburetor with carburetor cleaner. I did not ungang the carbs and soak the bodies. Currently have access to an ultrasonic. I got lazy and shoved half the carb into the ultrasonic and ran it and then shoved the other half in and also ran it with simple green. Not ideal.

Ill take a look at that link and look into cleaning the carbs again.

Running without an air filter (open carbs) will make for a lean condition.
Which will make the bike run HOT.
Also not well at higher RPMs.
 

Rebuilt the carbs again and unganged them this time and ran everything through an ultrasonic/used compressed air to clean em...damaged one of the #50 air screws (next to the main jet), so i am looking to replace it. I checked ebay but I am struggling to find it. Any thoughts on where to look? Maybe i am miss labeling the part?

Ok so it sounds like you have a set of carbs that have only pilot (or fuel) screw and not an air screw or both.  As pilot screw only carbs (vm22 or vm24) came with the additional #50 pilot jet.  I have removed the additional #50 pilot jets from several different sets of carbs and have not noticed any difference in operation. So if you can not find another one of them I suggest pull all of them.

You should be making use of some type of air filter or as stated it will run lean without some jetting changes. Filters also limit the amount of dirt and other things getting sucked up into the carbs and cylinders.

Sweet, thanks for the advice and the information on the carburetor. I am scouring ebay but its looking slim.

I have a set of K&N style pods on their way, when they arrive ill run the bike with them.

I forgot to mention in my previous post. when i used compressed air a chunk of goopy fuel line flopped out of the fuel connectors between the #2 and #3 carb bodies. Fingers crossed this solves it.

If you are going to run pods on it it will still mostly be lean. The pods will flow more air than a stock air box and filter.

You said K&N style pods? I hope you mean genuine K&N, APE or Uni filters. Some of the cheap ones are poorly designed and can introduce new problems like blocked air jets in the carb mouth.