I have found my roller which is a home built 30" diameter by 7' water filled (about 300# per ft) does a nice job of smashing things flat in the wet spring but that by the middle of August the soil has revived itself into its rougher preferred state. I think all I am doing is flattening it temporarily and then the grass roots and and other entities within the soil are working against me.
Personally I would mow it short, let it come back alive and spray it with an effective weedkiller to take out the root spreading weeds, and then use the box blade a couple of different directions with enough bite to take off the high points and spread them out. (May need to play with the angle, weight, and tine depth settings so that you have an effect without over digging.) Let this set for a week to get the ripped up plant matter dried out. Then broadcast seed and use a chain harrow or similar to lightly work the seed under and smooth it. ( A chain harrow with the teeth angled back will not plug if there is not too much loose vegetation.) This would not upset the soil structure and have any residual effect of tire compaction. It would also leave a lot of plant matter and soil and plant structure to act as protection from wind, washing, etc.. Then how you mow it will help control what type of grasses you keep long term, i.e. orchard, brome, and other taller, coarser grasses do not like getting cut on a regular basis and will give into the finer grasses that are more lawn type. Mow less often and the coarser grasses will overgrow and shade out the finer grasses.
This would work better in the fall when the grasses are not growing so rapidly which essentially gives you more working time plus you want to target a time for the seed to germinate and root so it will root all winter and then start the mowing in the spring as desired.