Does anyone here use the solid form jet dry baskets? If so, how many washes do you get out of one basket?
No, not recommended since it desolves during every wash and rinse cycle instead of just the last rinse cycle. Besides wasting product, it also runs counter to its intent - it hurts washing performance if you add rinse agent to it. Kind of like adding conditioner to your shampoo, or liquid fabric softener to your laundry detergent. The soap/detergent is doing its best to clean off the Jet Dry et al.
I don't think rinse aid and detergent would work against each other. After all, both contain surfactants and there are some detergents with rinse aid (substitute) available. These rely on an extra-heavy dose of surfactants that are supposed to last through the interim rinse(s) until the final rinse.
Here's an current discussion on JD:
Here is a link that might be useful: JetDry Solid - 4 Washes and it's almost gone!