When did this behavior show up? It could be related to a rodcap installed
backward, eccentric timing gear, etc.
I assume that by "maybe twice per firing order or so" you mean once per
crankshaft revolution. Maybe you should mark the point on a pulley
or something.
Other things to look for might be something too close in the bellhousing.

If you turn it over fast, do you or do you not get a "clunk"?
(This is critical.)

Good practice is to turn the crank several revolutions at every step along
the way so if something shows up, you know what you did just before it
started, and thus don't have to undo so much.

These "domed" pistons - do they have anything that projects up to where
the cylinder head is flat?
--
George Downs, The "original" Walrus3, Bartlesville, Oklahoma