Well, this is what I ended up doing that I'm pretty happy with.
I went ahead and used both on the 10 gallon tank. For the first one, I used the stock filter cartridge, mainly for mechanical filtration. The second one, I didn't use the filter cartridge and instead just filled it with ceramic bio rings. I made sure to use the cycled bio rings that were already in the internal filter, and also added about five times more. This was way overdue, but I'm very happy that I finally got it taken care of.
I went ahead and used both on the 10 gallon tank. For the first one, I used the stock filter cartridge, mainly for mechanical filtration. The second one, I didn't use the filter cartridge and instead just filled it with ceramic bio rings. I made sure to use the cycled bio rings that were already in the internal filter, and also added about five times more. This was way overdue, but I'm very happy that I finally got it taken care of.