I'm not sure what map I was looking at, but I'm actually in zone 4.

"I don't have an irrigation system, so that's why I'm not going straight KBG."

This makes no sense to me. If you are going to seed your lawn, then you need to keep those seeds moist 24/7 for at least 2 weeks, longer for KBG. In order to do this you will need to set up hoses and sprinklers. If you can do that why can't you water in periods of no rain? Hose is cheap, and so is a timer system, which you will need anyway if you are overseeding. MN is KBG country. PR and TTTF can suffer cold kill in MN. TTTF and PR use less water than KBG, but it isn't significantly less, and mature KBG can go dormant during times of drought, the other two will die. Despite what you have heard, KBG can be grown in shade. As long as you get 4-5 hours of direct sun, there are cultivars that can do well. The problem is the seeds that the big box stores carry are generally older, poorer performing varieties that have little if any shade tolerance. They choose the seeds for you, and they choose whatever they won't according to what they have on hand, and how much profit they can make. If shade is really an issue, I would then go with a 80:20 mix of TTTF/KBG, otherwise I would go all KBG, but choosing seeds from a reputable seed seller.