That isn't the "check strap" it would be the spring that holds the door open. The "check strap" is what holds the door from opening too far (early cars simply used a strap of leather). The "check strap" on a late model car does both hold the door open AND limit how far it opens.
The way your Chevy trucks door swings outside the body is going to make using the late model Toyota type check straps unusable as far as I can figure.
I remove and install those check straps almost daily and they don't have much movement other than straight in and out. They just won't work for your application.
I think you need to maybe find another source for your springs or something. I have been running the original ones on my truck and they work fine.