Did you cut half an inch off the end of the tubing when you attached it to the new water level switch. If the hose is in good shape, this should ensure a good seal at the switch. It does not take much of an air leak and it can be intermittent. If the hose is stiff or has small what look like cracks running along it replace the hose.

Another possibility would be something floating around in the bottom of the tub and every once in a while it partially plugs the hose.

It is very possible that you have a small hole in that plastic hose. Go down to yor local hardware store, and bring the hose with you, and replace it. That has to be it. Because you replace the water level switch. The hose is cheap. Do it, and let us know. Tom ApplianceEducator.com

Good Luck. Tom ApplianceEducator.com

"On the rinse cycle it reverted back to the old way of not stopping to fill."

Unless I have missed something in one of your earlier posts this is a new symptom. I thought the only problem you had was it overfills.

This is starting to look like a bad timer.

I can understand your frustration, you have been fighting with this sucker for quite awhile.

Some of the below you probably know already but figured it wouldn't hurt to include it.

The water level switch has a Common connector for the Normally Open (NO) and Normally Closed (NC) contacts on a single switch.
When the air pressure in the tube becomes high enough the switch closes.
There is an air tight diaphragm in the level switch which moves back and forth to activate the switch.
So when you start a wash the NO contacts are open and the NC contacts are closed.
The NC contacts are connected to your water valve and a set of contacts in the timer puts power to the common connector of the level switch.
So the water valve is actuated and the washer begins to fill.
As the water rises in the tube, the air pressure in the tube increases until it is high enough to trip the switch.
Now the NC contacts open, stopping the water. The NO contacts close starting the agitator/motor and the timer motor.

This does get more complicated when you get into rinse cycles as timer contacts are used to redirect power as required but the basic fill is the same.

Trying to find wiring info on Kenmore's is difficult if not impossible unless you are a Kenmore tech and I do not have any.

I would replace the tubing. There is no guarantee that this will fix it but at least you will be able to eliminate it as a possible cause.