Typically a backfire is a lean condition, thus your checking and cleaning the petcock filter is a good move. If the valve adjustment went out due to a locknut or two coming loose can spell damage if the cam were to feed in even more clearance, or burning a valve when it goes too tight. Hopefully you are not going to see it increase the clearance when the nut backs off due to the twist of the threads and vibration. This would be a possibility. But, I don't think I would expect this to happen.
Still a quick visual and check of the nuts will likely be tight.
I would check the points after I check the valves...then I would look at the carbs for debris in the fuel bowls. If you find any then you need to clean the carbs and figure out where your debris is coming from to stop it. Some fuel line can come apart with age or being the wrong type of fuel for that line. This is especially true on some rubber parts not liking the ethanol in fuel. It took a bit of time to get carb parts and fuel lines that would not be destroyed by the "new" fuel blend.
Maybe this is at play?
Are your float levels correct for the model carbs you have? 550 FAQ has info.
Could be related to inadequate fuel in bowl or restriction in amount of flow. Clear tube method is easier to determine the float level...just can't verify it when running at high rpm.
A partially clogged emulsion tube can cause the fuel draw to fail to deliver the fuel volume needed. Or a blocked main jet...clogged. So, I would pull the main jet and the emulsion tube is beneath this... pressing on the emulsion tube with a screwdriver tip should dislodge it... check your jet size if you don't know it. Write it down in your maintenance log or maintenance manual where you are going to find it when you need it.
Pay attention to the orientation of the emulsion tube as it has to go back in the same orientation.
The emulsion tubes foam the fuel to increase atomization as the fuel is drawn out of the main jet. Above 1200 rpm the emulsion tube starts working.
that performs this work... The idle circuit is still there, it is the needle rising will be affecting draw and the emulsion/atomization if the fuel coming through the main jet. As the engine vacuum and air bleeds influence with the needle rising as the throttle is twisted open. The fuel level around and in emulsion tube lowers reveals more holes in the tube. The amount of fuel being determined in the main jet opening and the needle clip position.
So, check your valve setting, too tight (below the clearance setting) and valves burn...
Check your timing
Check your fuel filters for sedimentation.
check your fuel bowls for sedimentation, if fuel lines are old consider replacing, check float /fuel bowl level, check main and emulsion jets for any signs of clogging.
What clip position is the needle in and which model of Keihln carbs?