It depends on the conditions of your soil, but yes, mulching heavily is an option, and not one that should be looked upon with scorn. You will have to reseed everything you want later, but in the meantime, you will amplify your hugels' natural tendency towards acting like a worm and soil life generator. If you haven't already, you could cut a path around your hugels, tear up the grass, invert it atop your hugels, layer with partially finished
compost, dig out the paths and replace with ramial
wood chips, and mulch the tops of your hugels with the same.
Also, how bad is it to have grass in the mix? You can easily incorporate lawn grass into a meadow/pasture mix and use it as living mulch, or incorporate it into a chop and drop green manure regimen.
Finally, you could find something likely to outcompete the grass, anything from squash to physically shade the ground with its large leaves, to buckwheat, which grows quickly and hosts nitrogen-fixing bacteria.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein