What attachment might be best to use?

[Slowpoke Slim]

I would look to use a heavy drag type harrow of some kind.

Chain (as in "chain harrow"), or a large railroad tie pulled along by a chain coming off each end, and pin that to your draw bar and drag the field with it. The more passes you make, the better it will get.

The heavier, the better. But a heavy weight chain harrow would probably do the job. If you look up "chain harrows" on the 'net, you should see what they look like. An 8' or 10' wide heavy duty chain harrow won't be "super cheap", but cheaper than a disk, or plow-then-disk.

 

[Rustyiron]

Half a day with a SS and a good operator.
The root mass of what you're mowing is going to be difficult to deal with for lighter tillage implements. If you're not concerned with spending a couple grand and are "building" your collection of tractor tools, as others have suggested a good (heavy) land plane will do it also.
Dry conditions will be an advantage to help separate the dirt from the grasses roots.