Oil weight and car smoking

The stock modular motor is set up for thinner oil. Don't recommend going any heavier than 30 weight. The only exception to this is if you have a built motor and the motor's builder recommends heavier oil.

IMO, consider that your symptom matches that of worn valve guides. The oil escapes down the valve guides while the motor is stopped. It pools on the back side of the intake and exhaust valves. It gets burned up when the motor first starts. This also explains why it doesn't smoke when hot.

A compression test and cylinder leak down test will help confirm where the weakness is. Because if the rings are not sealing well, there is little that can be done short of over haul.

Ford puts 5W50 in the newer GT500s. 5W20 is a mileage-oil. It is intended to reduce pumping losses to help boost efficiency and fuel economy.

I don't think the modular engine's tolerances are so tight that it can't run a heavier oil. I've read that the HLAs (hydraulic lash adjusters or "hydraulic lifters") might pump up at very high RPM with heavier oils. I think 10W30 would be fine, even in winter. I've got 5W40 in my SC 2V and its fine with it.

Having said that, an engine with 194K miles has led a very long life indeed. If it's not making noise its bearing clearances are probably still within spec. You can probably still see honing marks on the cylinder walls... Whatever oil has been run in it has served it well. Changing to a heavier grade of oil to try to reduce oil consumption is only pushing out the inevitable. If the valve guides are sloppy or the seals are cooked then heavier oil is a mask. And 10W30 isn't exactly "heavy" so it won't really change the oil smoking a lot.

What are your intentions for the car? To keep it for another five years? If a basic compression and/or leakdown test were done and the motor turned out to be "tired", what would you do? Would you consider, say, a PI-swap with a used PI engine from a Crown Vic or Mustang?

In Australia they run 5w40 in modular motors that are built in the US.

Sounds like leaking valve stem seals or worn guides, changing oil weight or adding a bottle of snake oil wont fix it.

Keep in mind that at operating temp both 10W30 and 5W30 have virtually the same viscosity.

In winter stick with the 5W for cold start ups, but otherwise I would run
10w 40 conventional. Especialy if your using oil at an excellerated rate.
It wont hurt your engine at all.