Hell 300 sq ft hardly is a task. If you did actually rent a sod cutter to cut that small a section, you'll be able to cut it up in literally 10 minutes, so do yourself a favor and save yourself some money by renting that sod cutter for the most minimum time they have available.(Home Depot rents them out for $69 w/tax for 4 hours) If you could rent one out for an hour for cheaper then that, then I would jump on that.
Two weeks ago I sod cut my back lawn of nearly 5,000 sq ft. From there I rented a 10 yd dumpster and humped all of the cut up sod into there.(killer!!!)
If that's not enough, I just got done spreading out 15 yds of top soil over the 5,000 sq ft I'm working on, with shovel and wheel barrow (BY MYSELF!)
I would ask for no less then $1 a yard.