First, you could definitely shear down to about 1/2 inch. Your example, Japanese bloodgrass, here in zone 5 goes completely dormant and always starts the year out with a shearing to get rid of the dead leaves. Be gentle with this one, it has very shallow roots and pulls out of the ground easily.

Many of the other grasses not hardy to your area can be overwintered in a cool/cold area (garage or cold room) depending on what they can withstand. All but the tropicals (eg purple fountain grass) can withstand quite a bit of cold.
You might want to check with the group of folks on the northern gardening forum and see what they are managing to grow in the ground in your area.

I overwinter a few bamboos in my garage & keep the garage around 0 to -2C for most of the winter with a small heater.

good luck
A.