2 ideas come to mind
1. $5... Bring a couple 8" long Black PVC pipes, zip ties and a bungee. When you get wherever you are going (assuming you're fliying...?), go to the loading dock of a store and "borrow" a milk crate. Zip tie the PVC "rod holders" to the corners of the milk crate, and bungee the whole operation to the kayak through the back scuppers.... Just use it for gear / rod storage or fly lining out of gear with the clicker on... if it holds tight. Don't forget to return the milk crate for good karma.
2. These might be able to be shoved into the scupper holes... just don't let the rental company see it, cause you could potentially "damage" the scuppers. If you fish it in gear go VERY light on the drag.... and don't do it on your own kayak.
I'd go with #1 over the seat with rod holders idea.
I'm sure DSafety and others will debate ... but I'm a risk taker and enjoy it.