I would go with all KBG (Kentucky bluegrass) except for areas of heavy shade, where I'd transition to creeping red fescue. I'm not very good at picking specific varieties of KBG, but I think KBG is a better choice for central IN than a mixture of KBG and rye. You can seed into an existing lawn. If you can core aerate first, you'll improve the seed-to-soil contact. Absolutely mow lower before seeding. mowing low does a couple of things. It helps get better seed-to-soil contact, it helps more sun get to the new seedlings and it gives the new grass more time to root before you need to mow the existing stuff. And bag the clippings this time since you don't want them blocking the contact with the soil. If you're trying to keep most of the existing grass, lower the deck gradually (maybe lower one notch and mow, wait a few days, lower another notch and mow, etc until you're mowing as low as you can take it). If you'd rather have the new grass mostly take over, lower the deck all at once and scalp away, stressing the heck out of the grass. I've rarely covered new seeds with anything, but I probably would have had better results if I had.

I'd wait until it hits 3" and mow it down to 2, then keep mowing regularly to encourage thickening, until the cold slows the growth. As for thin areas, you can also hand core aerate with something like a Turf Hound for small areas that need prepped. The problem with just spreading lawn soil over your turf is that you might get a layering effect which is not stable. I'd rather core thin areas--with or without topdress.

Turgeon has an interesting perspective on phosphorus (P). When you read the quote below from Turfgrass Management, keep in mind there's a difference between available P in the soil and unavailable P in the soil (in other words, P in the soil that's available to the plant and P in the soil that's unavailable to the plant). Together they equal Total P. I guess the "available P" in the soil is the phosphorus that the beneficial fungi got in them and trade with the plants in exchange for exudates the plant's roots give to the fungi. There's a symbiosis there between plants and fungi. Each wants something the other furnishes. Turgeon: "The phosphorus concentration of dried turfgrass clippings is usually less than 0.5% compared with 3% to 5% for nitrogen." "Phosphorus deficiencies are most evident during turfgrass establishment. Generally reduced growth, dark to reddish leaf coloration, and narrow leaf blades indicate a deficiency in available phosphate in the soil. A soil concentration equivalent to 30 pounds per acre of available phosphate is considered a minimum level for turfgrass growth." [That's roughly 0.75 pounds per 1,000 square feet--we'll round and say 1 pound per 1,000 square feet. That's the minimum needed and I'm guessing the vast majority of soils have that available. Back to Turgeon again below.] "As phosphates are relatively immobile in soil, they do not leach readily from the turfgrass root zone. Many turf soils that have received liberal quantities of phosphorus-contaning fertilizers are, thus, high in total phosphorus. However, the plant-available phosphorus concentration in the soil solution is usually a small percentage of the total concentration due to the rapid rate at which phosphorus becomes tied up in insoluble forms. The phosphate ion (H2PO4-) combines readily with iron and aluminum cations to form insoluble compounds, especially in acid soils. In many instances the amount of available phosphate in the soil is surprisingly low compared with the amount removed by actively growing turfgrasses. This is apparently due to a dynamic equilibrium between soluble and insoluble forms of phosporus; as the available pool is reduced by plant uptake, some ot the insoluble phosphorus becomes soluble at a sufficient rate to sustain turfgrass growth requirements. On many turfgrass sites where clippings are not removed there may be no need for phosphorus fertilizer as long as the residual supply from previous fertilizations is adequate."

I believe they are required to place a label on the bag of grass seed. So, if they can't tell you on the phone you might just have to drive up there and look for yourself to see what each bag contains. I think you should just spend the year mowing high and often, watering infrequently yet deeply. Get a soil test and work on amending your soil to bring it into optimal conditions for growing grass between now and next summer. When the summer is coming to a close, kill everything with round up. This is also the time to install some irritation if you want to do that. When everything starts to look dead, scalp the lawn and clean up all the dead mess. Water the yard like crazy to encourage weed growth. When weeds start to grow, blast them with the roundup. Lay down some compost and broadcast yourself some quality seed. Lightly rake it into the compost. Keep it nice and moist for the germination period; for KBG, that is about 3 weeks. Then go ahead and apply a fertilizer treatment using a starter fertilizer. Water as necessary to return to the deep and infrequent. Your first mow for KBG should be when the grass is over 2 inches; set your mower deck height for 2 inches. After that first cut, start gradually raising the mower deck to the 3-4 inch range. This should carry you through the end of fall. If it have some nasty things growing in there like creeping Charlie, chickweed or oxalis, spot treat them with Tricloypter using a pump sprayer on the finest most setting. Don't treat the entire yard, just the specific weeds. You could probably do one more fertilization application before the year would be over to winterize the lawn. Do this when the grass is no longer being cut at your normal mowing height, but before it goes dormant (it is still green but not growing taller).