Oil pump hell.

Recently - I noticed smoke out of the exhaust. I've also noticed dirty plugs and an oil film inside my new exhaust pipes.

I hope you read this and understand that others have indicated what the possible problems are. So far, you want to waste time & money replacing a oil pump. Which is not the problem.

Smoke out of the exhaust, dirty spark plugs, oil film IN the exhaust pipes, are the listed problems. The possible causes are already listed.

Bad piston ring sealing
Bad intake to cylinder head sealing
Oil getting past the valves by way of the guides which is due to the valve seals allowing oil past them. They are most likely dry rotted from sitting.

I have NEVER heard of pressure waves created from an oil pump, much less issues from that.

Now, go and pull your valve covers and intake. Check the cylinders for poor wear & scores. Take note of the intake manifolds runners at the cylinder head, look for black/blackened oil residue. Check the cylinder heads valves seals. Replace as needed. Reseal and have fun.