Note there are Two Size Valves.

And they are called 3/4" and 1" ,
but BOTH have 1" piping connections on the REAR.

So, the fact that you have 1" piping / fittings,
has NOTHING to do with whether your valve is the "Standard 3/4" or the "Large 1" Valve Size:

REFERENCE the following:

3/4" Standard, ( 5 screws hold Valve Cover to Valve Body ).

Or
1" Large. ( 8 screws hold Valve Cover to Valve Body ).


And they use different size Seal Kits and Rotor Discs ( and Valve Body, Valve Cover, By Pass, etc ).

Standard 3/4" Rotor Disc is about 3 3/8" in diameter,

OR
Large 1" Rotor Disc is about 4 3/8" in diameter,


The Standard Version Seal Kit ( 7129716, WS35X10005 ) we sell is commonly used and smaller in size than the 1" ( Large ) valve version, so please check before ordering.

And the LARGER SIZE:
The Larger 1" Version Seal Kit ( 7185487, WS35X10020 ) is a full 1" larger, so please check if you are not sure before ordering.

For Model Number Reference, as to whether yours is 3/4" or 1" Valve design, see the Service Manual Listings on our website,
SEARS - Kenmore
or
GE Smartwater
or
Whirlpool

Also you should take a look at this animation from the Morton softener site - the link is below.
Their softener is another variant of the Ecowater/NorthStar/Sear/GE Smartwater type system.
The animations are almost identical to the animations on the Kenmore site, except the Morton animation also
shows the flow paths, dis-assembly and reassembly of the complete valve body, including all the o-rings.
It also shows the complete float assembly - Kenmore site doesn't show either of these assemblies last time I checked.

After the link is pulled up you have the option to run program - I had to click the button twice
- may just be my browser but I figured I'd mention it.

Morton System Saver Water Softener Animation; (Click Link Below)
http://www.systemsaver.com/morton-website/interactive-animation/index.htm