See if you can find some Bacopa monnieri, it's native to Florida and when it is emersed it does something very similar to your pic of what you thought was HC. It won't work well as a forground plant though, but it will grow in your aquarium. Most plants take a much different form emersed than they do submersed. Our bacopa (I'm in Ft. Myers) is often growing aside hydrocotyle umbellata, which will be found tangled under water, climbing the banks along with the bacopa, and can even be found growing in the grass of your front yard. I've yet to try and grow H. umbellata in an aquarium, but it's probably possible to train it to grow like H.verticillata which is a pretty cool forground plant when grown under high light.
Here is a pic of our bacopa as it grows in about six inches of water, it stands straight up in deeper water as you can see in the second pic growing with H.umbellata...
Here is a pic of it emersed...
Here is a good pic of Pilea trianthemoides for comparison, it's leaves all sort of curve forward and they cluster on top of one another like it seems the ones in your pic do...
This link may be helpful to you, you can find most native and even invasive Florida species on that site. You can go outside and find a lot of what is being sold in the pet stores, including Ludwigia repens and different species of Valisnaria.
All mosses are emersed marsh plants like many plants adapted to aquaria and common in the hobby. Whether or not it will acclimate to your aquarium will only be known if you try. It's often too hard to identify species without a microscope, definitely too hard to tell from the pics, but it does seem to be some kind of liverwort.
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