Got the cams out today (they were a bit sticky!), and have measured the old shims and ordered the new ones. Hope to have the car back on the road next weekend!
I'm curious: why/how do the tappets and shims get out of alignment? I can sort of imagine how they could be loose (lots of spinning wearing them down??), but how do the clearances get too tight? Expansion of the metal over repeated heating cycles?

Thanks! I haven't been in this part of the engine before and am curious how it all works.

 

The shims do get compressed slightly where the valve steam contacts them, but also the valve seat wears, where the valve contacts the cylinder head. It's not so much the shim wearing, but the valve recesses into the head and that tightens up the clearances.