Had this problem a year ago. Work backwards from the problem area.
Hot/cold air flap working inside the dashboard?
In my case, it was my 2nd guess; heatercore was so far gone, RMI25 and tens of flushes made no difference, but a new heatercore did the trick ... pretty much. Flushing the rest of the cooling system is never a bad idea (back and forth is how she likes it).
Besides the stock 180°F thermostat, there are now LT1-spec thermostats available in 195°F and 205°F.
It goes without saying that your fans should be programmed to work with the thermostat you selected (I suspect you are or were using a 160°F?). The later your fans come on, and the less air flowing through the radiator, the hotter the antifreeze gets, and the hotter the air blows through the heatercore and into the passenger area.
Partially covering the radiator is a time tested and proven trick. Start small and work your way up.
If it's that cold out, you don't need an external oil cooler. In fact, according to GM, if you're using synthetic motor oil, you don't need an internal oil cooler either. Many many years ago when I owned a 9C1, covering the external oil cooler made a difference. Deleting it made a bigger difference. Oil cooling seems unnecessary unless it's above 85°F and you sit around or stop & go a lot. Mobil1 0W40 or Castrol 0W30 are my preferences.
If the problem is your electric water pump, try a new or a different one. My Meziere HD never gave me any problems, except when it quit working. I changed it by myself on the shoulder in about fifteen minutes, and was back on the highway. Try that with a mechanical one.