There are wide mouth mason jars that are a good bit shorter. Can't say for sure, but I think the one below would allow the current stem to sit pretty much in the bottom of the jar.
This one specifically: http://www.amazon.com/Loew-Cornell-Ball-Mouth-Canning-Package/dp/B00KF5STQC/ref=sr_1_4?ie=UTF8&qid=1446598621&sr
I found them on Amazon! I got these ones:
https://www.amazon.com/gp/product/B00KF5STQC/ref=oh_aui_detailpage_o02_s00?ie=UTF8&psc=1
I got them at Target but these are the exact same ones on Amazon.