I love hornwort and have tons of it. I think it is a beautiful plant and always wish that I could manage to get it to grow upwards from an anchored position at the bottom; I've read about people who have managed to get it to work what way, but I have never had success.
Trying to root it is IMHO a complete waste of time. The part that is buried always seems to die and rot. The lead weights work a bit better, but if the bundle is kept together it looks bad, and if the stems are separated each one will need an anchor. I just don't like the idea of that much lead in the tank.
Tying it to driftwood or rocks, as one would normally do for Anubias or Java Fern, is unsightly and awkward. That method works with those other species because they are "neutrally buoyant" and aren't trying to float upwards, and also because they are relatively slow growing. The "best" method with Hornwort for me has been to take a long stem of it, at least a couple feet long, and just loop it around some driftwood so both ends are floating upwards from the wood. These long strands are usually branched, and with a foot-long branch on either side of the wood, stretching upwards, it makes a very pretty display. Might last for weeks or even months before the bottom part weakens and breaks, but Hornwort is such a lightning-fast grower that if you have it you must simply resign yourself to the fact that you will be trimming, pruning and discarding a lot of it on a regular basis.
Maybe you could try Guppy Grass (Najas). It's just a loose mass of intertwining thin leaves and branches, not as structured (or as attractive, IMHO) as Hornwort, but just as easy and fast to grow. It doesn't float upwards nearly as much as Hornwort, and a bunch can easily be snagged or hooked around a piece of wood or rock and will then spread in all directions from that spot, rather than just straight up.