Due to government regulations, washers that use full loads of water automatically (ie. non-High Efficiency washers) are not allowed to be produced and sold anymore. Your best option is to purchase a Kenmore top-load washer with the option of Deep Fill and a second rinse. Government regulations also prevent the Deep Fill option from being used on the Normal Cycle.
There are also government regulations on how much water a new dishwasher uses, which is why new dishwashers take twice as long to clean.
This is my suggestion for you: sears.com/kenmore-22352-4.2-cu-ft-top-load-washer/p-02622352000P?sellerId=SEARS
It has Deep Fill and the Deep Fill will fill the washer to the maximum level.
Matching Elec Dryer Model: 65132, sears.com/kenmore-7.0-cu-ft-top-load-electric-dryer/p-02665132000P
Matching Gas Dryer Model: 75132, sears.com/kenmore-7.0-cu-ft-top-load-gas-dryer/p-02675132000P
Kenmore 21112, 31312, 21652, 31652 washers have a different kind of Deep Fill that has four water levels: “Auto”, “Medium”, “High”, “Max Fill”. Again, due to government regulations, "Max Fill" will not be able to be used on Normal Cycle, but "Medium" and "High" are available. On these models you can increase the water level on each Cycle. For a depiction of water levels see page 2 of the Quick Start Guide: i.sears.com/s/d/pdf/mp-tc/10130653/prod_24761283312
For those Kenmore washers: sears.com/appliances-washers-top-load-washers/b-1101278?Brand=Kenmore&Brand=Kenmore%20Elite&filterList=Brand&sortOption=UNITS_HIGH_TO_LOW&searsTab=true
Hope this helps! If you have another question, just ask.
Don't purchase any washer that doesn't have a Deep Fill option as you will not be able to control the water level at all with those models.