Oil Flow check- when you pulled off the valve cover, did everything look wet with oil? Was there pools of oil laying in the cylinder head around the depressions in the cylinder head casting? If .everything looks wet, you are probably ok. You could run the engine without the valve cover in place but oil will be flying around and things would get messy. Turing it over on the starter without ignition and you may see the oil weeping out from around the camshaft bearing pedestals/ bearing caps.
It's interesting that you had to readjust shims in #3 exhaust and #6 intake since the firing order is 1-5-3-6-2-4 where #3 and #6 are beside each other in the order. Did you follow the camshaft installation procedure exactly as written in the manual? if not , you may have bent a couple of valves.
#1 and #6 pistons must be at top dead center
The exhaust camshaft is installed first and the exhaust cam timing set.
Then the intake camshaft is installed and tightened down and this is where things get critical because when you tightened down the exhaust camshaft nothing would have interfered with any of the valves or the pistons provided that the pistons were in the right place BUT when you go to install the intake camshaft, if the pistons and the exhaust camshaft are not in the right place, as the intake camshaft gets tightened down, valves could touch each other and bend a valve, and I wonder if this happened because you had to reshim #3 exhaust and #6 intake.
What size shims did you take out and what size shims did you have to install in #3 and #6 ??
Bent valves on a cylinder head install has happened here 2 or 3 times in the last 5 years and I suspect it happened because of the lack of understanding of how close the valve heads pass each other as they open and close Hemispherical heads are known for bending valves when a camshaft falls out of timing when it jumps one tooth on the cam chain and one tooth of timing on a camshaft represents 20 degrees of crankshaft rotation. So think of that. If anything was out of time by 20 degrees when installing the camshafts, you take the chance of bending a valve. In the Service Manual, Kawasaki tells you to rotate the crankshaft 2 full turns by wrench after getting the head and camshafts installed and if you feel any interference at all, you have to rotate in reverse and recheck the timing. I wish Kawasaki did a better job of emphasizing this point prior to providing the procedure for cylinder head installation.
If you have a cylinder leak down tester, i would check #3 and #6 cylinder
good luck and let us know what you find