What else do you have in your cleaner apart from Coco Betaine?
In my experience salt works reasonably well sometimes but not always -- you will probably have to experiment. I had better luck with adding it in a solution than directly.
You could also try crothix if you happen to have it, or maybe some kind of gum (like xanthan gum)?
Or, just put it in a foamer bottle and then no need -- that's my favorite .
"...Does it have to have a sodium based surfactant for the salt thickening idea to work?..."
No, it doesn't have to be a sodium based surf.
If you're wondering whether salt will thicken the product, why aren't you experimenting with a sample and finding out? Sounds like you have the product on hand to work on.
Another tip -- If you find out that salt works, you'll have to experiment to find the correct dosage. Too much salt can be worse than too little.