[wiswind]

If you can take the oil pan off to check the oil pump pickup screen, that would be a good idea.......however, at least on my '96, it is a lot of work due to needing to remove the "Y" pipe......which is the assembly that includes the catalytic converters......
If you remove the "Y" pipe.....support the front end of the flex pipe to avoid breaking the "flex" part of the flex pipe.

I am thinking that there might be junk in the oil pump pickup screen......the other option would be super worn bearings.......

If you have much coolant leaking into the cylinders.....you want to watch out for hydrolocking.......coolant does not compress like air.....
If you have worked on cars as much as I am guessing you have.....you know about that better than I do.

I certainly hear you on the time to super clean things up on other people's cars........that is more time....which is money out of your pocket.
Many folks don't realize.....most repairs.....Labor is the most expensive part.

Some have a oil level sensor....which is mounted on the oil pan above the oil drain plug......I do not seem to have one on my '96 3.8L.
The other thing would be the oil pressure sensor, which is located where you cannot even see it unless you remove the big alluminum bracket that the alternator and power steering pump are mounted on.
I have the oil pressure sensor (actually a switch) shown in a picture "a look under the power steering bracket".
I thought to take a picture showing it while I was changing the power steering pump.

I have not had my oil pan off........but it looks like it would not be a lot of work....EXCEPT for the "Y" pipe.
There have been a couple of posts about oil pans rusting through and leaking......so give yours a look.....because if you are going to go to the work of taking it off......it would be the time to replace it if you see significant rust.
I would think that they would rust from the outside in........if it was from the inside out.......then I would think that some other issues would show up long before it rusted through.

One trick that I do when starting my car up after changine oil and filter......I remove the fuse for the fuel pump.....and crank the motor in 5-10 second runs until the oil pressure light goes out.
This gives the oil system a chance to fully prime before running the motor.