Mosin... Before you rip it apart, check your clearances again (back of the cam, valve closed) and run it gently with the valve covers off. Observe the rocker movements and squirt oil onto the valve stems, through the valve spring coils, as it ticks over. Maybe it just needs a few minutes of well lubricated running to get the valves closing as they should. You can also check oil feed to the valve gear at the same time. If it is a case of head off, check for bowed pushrods, and also their fit into rocker and follower cups. They should not bind, but still be a snug fit. Most unusual for a pushrod to jump out if all assembled and set up correctly. If the motor is A10, any chance they are A7 exhaust pushrods, masquerading as A10 inlets? Dimensions are somewhere out there, so you can see if you have the right pushrods. Clutching at straws here on your behalf, worst case is a bit of work and a new head gasket. Plus the ever popular re- seat the pushrods game.
Good luck, Swarfy.