Welcome,
Its pretty unusual to something like that that shows up at speed, rather than RPM.
Are you absolutely sure it's motor oil? I would have thought the valve cover job would have sewn that up. Since it's variable, perhaps its the PCV valve at the back of the block. It's supposed to separate oil from vapor, and when it goes it does funny things like whistle, weep oil and smoke. PITA factor is high since it might not be it, but on the bright side you can soak the old one in some gas to see if it's it, before you buy a new one.
Otherwise, oil sometimes comes out the back "crescents" on the valve covers, and the only thing that cures it is gobs of permatex red.
Also, it sometimes accumulates in the "valley" of the block. If so, oil will be plainly visible on the torque converter when looking from above with a flashlight.
You could take a look under the oil filter reservoir as those o-rings eventually bite through the hoses.
You mentioned "oil fill tube." We don't have one of those. We have the cap on the passenger side of the block, and if that seal on the cap is shot, that could be it. If you mean the oil level tube, that thing is bulletproof.
You didn't mention if it was stick or automatic. If automatic, the pipes flank the tranny, and any tranny fluid leaks have a tendency to drip right on top and burn rather than dripping on the garage floor. Same with the tranny fluid cooler lines, at the back of the block underneath the coolant reservoir.
I suppose you could have a leak on the upper half of your timing chain covers, although I have a hard time imagining how it would start.
Power steering fluid is always leaking somewhere on these cars.
More Clues!
o/______\o
(Oo=00=oO)
[]=****=[]