Good result!
Most diagrams you'll find online do show the push-pull on the tone pot, however you can use the push/pull pot on the volume the exact same way. Just connect the wires shown on the tone pot version to the switch portion of the push/pull volume pot. Think of the switch as a separate entity (even though it's physically connected to a pot).
I'm going to be doing the same mod to one of my teles, except I'm using a push/push pot.
Here's a good video:
https://www.youtube.com/watch?v=7hHPxAQu4NA
And remember you need to ground the cover of the neck pickup separately (covered in the video).
EDIT TO ADD:
Not to split hairs here, but technically the mod is "series switching" not parallel switching as you stated above.
The standard tele switching configuration puts the neck & bridge pickups in parallel when used together already. The switch (via push/pull, 4-way etc) puts them in series.