Don't know about Zodiac stringers, but most other brands have rubber stringers endings, if without them will end abrading tube fabric, when sib is correctly inflated to al least 3.0 psi will be pushed against tubes and will help to avoid traveling along to transom or bow when at use.
All medium range inflatables and up have 4 stringers (side joiners) must be placed at X patern :
facing each other...
Probably have 2 long ones and missing the short ones, post a pic of your floor set up. Have solved that huge problem years back, now I use 2 long single piece stringers, with well inflated sib gives a fantastic ride...