The keys to good seed germination are proper depth and good soil seed contact. Over seeding doesn't provide as effective seed to soil contact as the no till drill. Our soil Conservation Office has a no till drill that they rent at a very affordable rate. As advised, check with the extension service, soil conservation office etc. or at you local farm supply for rental. No till drills are heavy units and usually require a hydraulic remote as the machine lifts to transport via hydraulics. No till also decreases the amount of seed loss to birds and other seed eaters.
An alternative is to mow the pasture short then disc lightly, follow with over seeding then use a cultipacker to firm the soil. The discing should just rough up the surface there is no need to deep plow or create a vegetation free seed bed for most grasses. Most grasses need only a slight fluff on the surface to get started. there is some value in maintaining some of the original grass (dead or alive) on the surface to prevent erosion. The cultipacker mashes the seed to the soil for the seed soil contact. Then follow the fertilizer recommendations based on a set of soil tests that your Ag Extension Service can advise on how to complete. It will take some time to get the results but will save you some money on fertilizer because you will apply only what the grasses need.
Hard pan will take more work to break the surface up and a previous poster suggested subsoiling, whatever works to break the hard pan down to a few inches deep. Overseed, cultipack and fertilize.
We have about 100 acres of grass for cattle here in NC. The above is based on my 25+ years of working with grasses and other crops for cattle feed and grasses for lawns. Your results may vary based on geography and other factors. The no till drill will allow one or two passes over dependent on starting grass height and if the drill allows application of fertilizer. The alternative method above has multiple passes - mowing, discing, seeding, cultipacking and fertilizing-so fuel and time costs need to be factored in. We used the no till method this fall on pasture and on my lawn - it worked great.