Moving on to problem # 2.

Try disassembling and cleaning the carburetors, follow the SCOTCH tutorial, he is a true eminence on this topic.

CARB REBUILD BY SCOTCH

I ended up buying a repair kit, it didn't cost me much money.

DAMINEDING KIT
 

These kits appear to the "generics" sold on EBay and if they're the ones stated as being made in Taiwan, you're good to go !  I've been using them for years in many carb-sets I have rebuilt and they are GOOD !
Although ''79 carb rebuild" article is outdated in some details the premise is clear.  CLEAN, CLEAN, CLEAN !

I don't have anywhere near enough info about your bike so won't make any efforts to advise over and above what's already been posted, at this time.

giorgi3 wrote:

I just took it for another ride. ....
 Cylinders 1-2 and 5-6 sizzled. Cylinders 3-4 didn't.
Suggestions?




 

It occurred to me that...

Before removing the carburetors, when you ride your motorcycle and you notice that the engine only works with four cylinders...

Remove a cap from the spark plugs of cylinders three or four and with the engine running, place a replacement spark plug and check for spark.

If there is no spark, your problem is electronic, not carburetion.

Good point.  Cutting out at highway speed when it gets hot... it could easily be a coil going bad. 

check the spark-plugs by switching them and check the spark-plus wires.
Holger

I rode it around two times today. About a 10 mile loop each time. Strangely enough, I didn't have any issues. The only things I changed was I gassed up with 93 Octane yesterday, and I took the side car off the Kz1300. 

I ran it up to 6-7k RPM a number of times. Also drove at for several minutes on each leg using various slow speeds, mid-speeds, and high speeds. No issues. Oh well, I'm not going to change anything unless the problem resurfaces.

Thanks for all the suggestions.