360 LA getting oil in #3 cylinder.

Depends how it's routed, which is why I asked about pics, but the valve covers were already off.
If there's a bunch of excess hose ran high, and it's routed into the manifold rather than carb base, or something "custom" then possibly. Or it could be routed into the back of the plenum which just happens to drain into #3... Plus, it's probably the easiest and cheapest to rule out.

Sadly, it seems more likely the issue is deeper, but sometimes those things are tougher to determine without a teardown.

Broken rings came up, and that also seems like a reasonable suspicion. Hopefully not the case, but a compression test will tell a lot and I think I read it's planned to happen too.

Hope for the best with OPs folks. No car is more important than time with family.
PCV has just enough hose to plug in rear base of carb. Last night, I stuck my compression gauge in #3 and turned engine by hand. I know that's not the way to check but I just wondered if I could get anything. After the intake valve closed, there was a whoosh of air sounding like it was coming back up the intake. Then I repeated with #1... no whoosh noise. So I plan to go ahead and remove intake and at least that one head, probably both. But with family issues, I'm not sure when I'll get to it. But I will update when I find something. Thanks again to all, Carl