Another option you could try if you're dead set on growing stem plants in the tank would be to plant them in pots with a nutrient rich soil like ADA Amazonia or Tropica Aquarium Soil. If you go this route, the best bet would be to purchase net pots used for hydroponics (or you could just take a normal plastic pot and drill a bunch of holes in it, but thats a pain and the hydroponic net pots would probably work better), so the plants roots can expand out in to the regular gravel.
With that light on a 10 gal, you should be able to get a carpet (or close to it) by adding a few net pots of hydrocotyle tripartita (Japanese clover) and keeping it trimmed and/or tucking the stems in to the gravel as it grows. Clover can be trained to grow pretty much anyway you'd like it to grow and will creep almost like a vine, even on inert substrates, if trimmed properly.
epiphytes like anubias and java fern will grow just fine in normal aquarium gravel if their light and nutrient needs are met through the water column, so you could absolutely plant either species in the gravel with no additional soil amendments if thats your preference (although I would add a root tab or two just to be safe). Since you plan on using it as a betta tank, you might consider adding some floating plants as they are found in bettas natural habitat and would be appreciated/utilized by the fish to rest on and when creating bubble nests. If you were to plant a few anubias, java ferns, and moss on driftwood or lava rocks, with a nice mat of riccia growing at the surface and some indian almond or other tropical hardwood leaves on the bottom above the substrate, the result would be a very nice, low-maintenance, biotope type aquarium that does not require any changes to your substrate- And your Betta would be in Heaven!