The description "Flutter" just freaks me out.

If it means what I think it means, and it's doing it with more than one gauge, then one place think I would look is....
I would be trying to examine possible
areas for the oil to become aerated/filled with air bubbles or simply leak internally.

Definitely chase the easier stuff first. More oil, different filter, relief valve etc

I have seen RB blocks where someone with good intentions tried to improve the main oil feeds by drilling or reaming them to 5/16",
which caused the bit to break through the side of the webbing/huge internal leak. This begs the question....if the bearing has
a 1/4" hole in it, and the upstream feed is 5/16" or even 1"..............will it ever flow more than the 1/4" hole?
I repaired the block by reaming/press fit tubing.

If there is a loss due to an internal leak, it may be possible to observe it while using a priming shaft.
priming with the intake and valve covers off to observe flow is good advice you have probably seen before.
I would probably start there.

Less often discussed.....if there is something weird going on in the lower end, you might be able to find it by priming and observing
flow and leakage with the oil pan off also. This can be messy but is sometimes educational......make a stub oil pickup without a screen, clamp
a hose to the stub, drop it in a bucket of oil. Place the bucket of oil in a large, clean pan under the engine, prime away
and observe from underneath with the best lighting possible. If one pair of rods leaks a whole lot more oil than all the rest, definitely
wonder why. If a leak comes from seemingly nowhere, zoom in on it...could be a hole somewhere there isn't supposed to be.

Of course, this is cold.
If the issue only happens when warm, like a porosity hole that opens enough to leak only when it warms up.....it can be next
to impossible to find.