The blowing white smoke and milky residue on the cap indicate to me that your engine is never allowed to stretch it's legs.
Short hops in a car that is 5 minutes to the store parked, then 5 minutes back will lead to excessive condensation in the engine that is as the engine cools it creates condensation in the engine and exhaust. This can build up and form milky oil, and or excessive water condensation in the exhaust.
This is not to say that the Water Stabilized oil Cooler may have leaked internally, allowing a/f in the oil but you can test for that as well as blown head gaskets by removing the cap off the expansion tank, and tie a latex glove tightly over the opening, Star the car and rev it to 3000 rpm for 30-45 seconds. If the glove inflates and gives you the finger, then you can say that either the oil cooler is leaking, and or the head gasket is blown.
So I am not saying a blown gasket is your issue, but you need to test for it, as well as you need to get the engine up to temp to boil out the water in the oil and exhaust (20 to 40 minutes of driving).
For the rings and such, I would put a pint of Marvel Mystery Oil in the Fuel tank, and a pint in the engine and start the engine and let it work, drive it about.
I would change the Fuel filter, and over the course of a couple of weeks Start the car and let it idle for at least 20 minutes a day to allow the MMO a chance to work.
I would look at the timing or that the valves are sticking, even the timing if off can cause a valve or 2 to not be seated.
You can also pull the plugs and add some MMO to the Cylinders to allow it to creep down the rings and get rid of goo and gunk.
For all the Cylinders to be the same wet or dry, is a little bizarre to me, and more intune with some gooey stickiness internally.
I have seen many a engine come back to life once the goo and gunk is cleaned out.
Yes the little red gear inside the speedometer can slip on the shaft or loose teeth (usually happens when you reset the ODO while moving, (never do that) and the odo stops working.
Engines can be timed, CIS can't. CIS if it is lacquered up can have fits, that is where the MMO in the fuel system tends to de-lacquer things up.
Follow the timing guide at
www.cabby-info.com for pictures of the timing marks.
Verify that all vacuum hoses are tight and viable. If you can turn the idle by-pass screw with your fingers then you have a vacuum leak and need to replace the o-ring on it.
my 2 cents.