If you have a sickle (grass hook) it would be faster than gathering one at a time -- but it is still quite a bit of work.

But then the seed heads would fall to the ground and I want to collect the seed, not only to prevent reseeding there, but to put it in another area.

I use a hedge clipper when I'm just dead heading and don't care where the seed goes.

If there is sufficient distance between these plants and others, you'd need to lay down sheeting to collect the seed. Try to make it curve up a little at the outer edges to act like an umbrella- a few rocks or whatever. You can use any material you like depending on weather and circumstances - newspaper, old sheeting, plastic tablecloths or dropcloths. But if plastic of course it WILL hold water if it rains, you'd need to collect seed more frequently. This is probably a better way if you intend to cut all the plants down - you'll catch falling seed and stop it reaching the ground. The rest of the plants can be put somewhere warm and airy for any remaining seed to shed.