What do you know about this engine? The reason I ask is it has aftermarket pushrods which leads me to believe it's had some head and or cam work. Olds valve train is non-adjustable and improper head work can lead to lifter preload issues like you have. Also broken or worn rocker bridges, worn pushrods and worn rocker arms can also cause loss of lifter preload. You need to check all of the pushrods when their respective valves are closed.
As for the engine I can tell you what I was told about it. It was in the car when I bought it.
Oldsmobile 350 from a 72 Cutlass
Ported, polished, 5angle valve job heads. They are olds 7A heads
Edelbrock performer rpm cam, lifters, spring, intake kit.
Cam specs : http://www.edelbrock.com/automotive/mc/camshafts/oldsmobile.shtml
Harland sharp roller rockers
Petronix hei distributor
Flat top hyperutetic pistons (was told on here they don't make these pistons)
1-3/4" long tube headman headers into dual 3" exhaust