If the lash cap will spin freely on some of the valves and not on others means the top of the valves are either different sizes or worn, mushroomed, correct?
If they are mushroomed take a good flat fine mill file or a good quality honing stone and get rid of the mushroom so all the lash caps fit freely on all the valves
I use lash caps to prevent damage to the valve tips, not to correct the geometry of the rocker arms to valve tip contact patterns
If the rocker arm contact tip is not contacting the center of the valve tip and sweeping across the tip properly you need a better fitting set of rocker arms, correct
Years ago I bought a bunch of W2 steel and aluminum stands to be able to mill the rocker arm stands off of BB heads and use the W2 stands to correct the height and location of the single shaft rocker arm available back then.
I ended up hearing about Rocker Arm Specials (before using the W2 stands) who will correct the rocker arm location and tip contact problems with bushings and relocating the adjuster positions and relocating the rocker arm tip contact location on the original ductile iron rocker arms we use to use.
Later on I started buying new aluminum roller rocker arms from Crane and Harland Sharp, I was thrilled that the Harland Sharps didn't need fixing on the their roller tip contact patterns to the stock valves on the stock iron heads like the other brand after market rocker arms did
Mopar use to hold drag racing seminars back before they went bankrupt in 1980, they recommended a rocker arm contact pattern to the valves on all of their Mopar V8 motors of starting on the inner third of the valve tip when the valve was closed and having the rocker arm tip slide across the center of the valve stem to the outer third of the valve tip, basically around .100 wide, before trying to correct it
I continue to use that as my guide on rocker arm tip to valve stem geometry
I have one of my drag race motors with a set of Jesel paired shaft rocker arm set up on a set of Indy 440-1 heads
My next high effort motor has a set of B1-MC heads with the original single shaft 1.7 ratio rocker arm set up, that set up will be discarded in favor of either a T&D paired shaft ductile iron rocker arm with 1.7 ratio set up or the same set up from Jesel.
Those kits are adjustable on the stand heights to get the best contact pattern on the valve tips to the valve stems
They are not cheap though
EDITED,It is good that someone like Mike at B3RE has taken the time and effort to make a adapter kit that allows guys to use it to fix the stock stuff so it works better with any rocker arms