I've used the no plow before....Definitely pre-apply the lime at least a couple weeks out and try to work it in----- also mowing and or round up'ing the area is best but you need to get the grass off the ground however---- a controled burn maybe the ticket for you --- reguardless the Now plow must make contact with the soil---I'd try renting a disc or something to develop my seed bed.
This is what I do on a field about the same size-----
I cut the grass, 3-5 days later I round up the new growth. A week or so later I either burn it off or disc the old grass in. Then if I burned it, I cut the ground with either a harrow or a disc (tractor or quad pulled), I level up the seedbed with a tire-pallet drag pulled behind my 4 wheeler, I broadcast the seed and re-drag. Every couple of years I do a soil sample on that field and treat with lime as reccommended. For best results I apply my fertilizer to the patch before leveling out my seed bed...this prevents burning out seedilngs if the mix is a little strong and it puts the fertilizer at a level where it can be best utilized in the first growth stage.
It matters not the weapon nor its caliber, rather the caliber of the one who wields it.