Topdressing a rotation of materials on a yearly basis is extremely dangerous. Layering of different materials can cause problems with drainage and also rooting. I would try to find a material that represents a sample of what you would eventually like the rootzone to be and stick with that material.
I would not apply more than 1/4" of material at any given time. depending on the topsoil you have in your area, a 1-1-1 blend of topsoil-compost-"medium" or "coarse" sand is a potentially beneficial topdressing material. I prefer a topdressing between 65% and 85% sand when topdressing native soil fields.
Incidentally, never use a sand with more than 5% calcium. In my area, sands come from granite. A high calcium sand can again cause cementing of the soil.
If this is a high profile field with relatively little bare area, I would stick with a bluegrass blend. slice seeding does tend to stay where you put it. I would not be concerned with movement of the seed. In a perfect world, I would have done the renovation in the middle of August rather than now. With sports, you do it when you can do it.
I think you are putting the success of your renovation in someone elses hands if you are not in charge of the fertilizing of this field. I would try to take over the fertilization. If the fertility levels are in line and there are no problems with the rootzone, the only thing holding back the growth of this field is fertilizer. I would make sure this field gets at least 4 lbs. of nitrogen each year with approximately 1/3 of that nitrogen in the spring. As long as you have irrigation you could even go 5 lbs of nitrogen.
Effectively rolling the field doesn't mean compacting it like a parking lot. A 1 ton roller with the vibration off probably applies less lbs. per square inch than the tractor you are using for aeration, seeding, topdressing etc.