I really like what you are doing. I'm going to try it because it will give me something else to do with my Repens trimmings. I don't have any other recommendations but I think you should try giving it more light to bring out the red in the plant.
Most of your hygro species will grow emersed like that, though they may eventually (several months later) start to lose their underwater leaves. Angustifolia and the standard hygro compact both will have small purple flowers from time to time. Personally I prefer the leave structure of the angustifolia more
Cardinal plant will also grow emmersed, it tends to stay more compact in form though than what you have currently. I've also noticed it seems to like a bit more humid air.
AR is much the same as cardinal plant in liking humid air, in my experience it has more of a tan/orange leaves than the vibrant red it gets submerged
Penny wort also does fine, personally I think it gets a bit unruly and overgrown, but it also will shoot out little flower stalks that look like little whit pom pom. This one grows much more vine like than a true stem plant
Also take a browser through the riparium plants list in my signature, lots of other options I'm sure I'm forgetting about
The angustifolia actually stiffens up substantially when emersed, the stem also gets fuzzy like a tomato plant. The leaves for me get a bit shorter and fatter when emersed but otherwise keep the same general appearance as submerged growth. I noticed that it takes a while to transition to emersed if growing out of the top of an aquarium, buy once established with emersed leaves it takes off. And it also transitions back to submerged seamlesslyWow, some excellent suggestions there. Thank you! Penny wort would be a nice contrast to the other plants I have in that window but I share your concern about mess. I never would have thought of hydro a.; it just looks so floppy underwater! But of course all of these stemmed plants can stiffen up when they reach air.