I'd try staking and lassoing, or use wire cages around the lower 2 feet. You'll need about a 10 ft section to make a 3 ft diameter clump.

Also, trim back the outer culms at the base as they break and/or droop outward.

Another technique is to use remesh, the 6" square concrete reinforcement mesh sold at the big box home repair stores. Cut an approximate circle out of it and wire it to rebar stakes driven into the ground. Rig it about 2' off the ground, so the grass grows up through it. The growing grass will hide the mesh, and the mesh will support the grass.

I like that idea Donn! Hidden by the grass.

an adaptation to Donn's idea... You might be able to delete the rebar stakes. Just lay the mesh on top of the grass after it reaches about a foot or so off the ground. The grass will grow through it and the stems act together to provide the support.
A friend of mine uses a similar method with Geraniums, Sedums, Peonies, etc. It works great & you never see the support system after the first couple of weeks.
a.