The mx/operation delta between a pa-28 variant and a 182/pa-32 variant is not all that great imo. The biggest delta is the acquisition cost. If I could afford to capitalize a six seater single, that's what I would own today, even with the understanding that my Arrow meets my useful load needs currently (2+1, 400NM mission).
Considering the OP's willingness and ability to foot the purchase of a 100K airplane and considering the dismal state of the rental landscape of present day American GA, I'd say go for the six seater (i.e. your 20% mission) and accept the "waste" during the 80% operation. Renting to the 20% mission might become such a hassle that it becomes a hell of lot more inconvenient than whatever frustration may arise out of flying a Piper Six/Lance around solo. A 182RG might be a middle ground compromise there if you don't want to haul around that much empty metal and still be able to load up the growing family, albeit more cramped.
The difference in theoretical operating and maintenance costs between a wide variety of SE planes from 180-300 HP is just that, theoretical and assumes all things in be equal. That is not how our universe functions though. The 'all things equal' numbers are close enough that they both fall within the statistical parameters of both groups. In other words, if you end up with a pig copy of an Archer and run it hard to make speed, it will end up costing more than if you had nice copy of a 260 hp Bonanza and just cruised along LOP with the power just coming in the pipe; you end up 25 kts faster as well. On the flip side, if you have a pig model of a 300hp Bonanza and run it hard to make speed, it will eat your lunch harder than any Archer has the ability to.
There are so many variables involved including operations and just chance luck that to try to make an accurate cost comparative analysis without looking at the actual airframes being considered, I would thing the task near impossible.
Define your mission first, buying an airplane because it is cheaper is not a great value when it doesn't do what you need it to do because your cost:benefit ratio is smaller, and the price of the ante into aviation makes it a steep hit.
Get the plane that does what you need, and trust you'll have the money, that's what I do.
Seriously, in my position with what I do in a feast or famine industry, I am either in the position to do aviation as I want to with no real concern for cost, ie it doesn't hurt to spend the money, I have plenty of excess income. Either that or I have no excess income for personal aviation at any level, I've done enough, thrill factor alone is not enough to justify it. Besides, during those periods I have a buddy with a really sweet Comanche that comes down and keeps me current in IPCs and FRs, plus every now and then someone needs me to run across the state and deal with a boat and they pay for me to rent a 172 and go.
That's also why I don't finance, I don't want that continuous liability. When I wasn't flying my 310 it didn't cost me a dime because my buddy in Atlanta just stuck it in his hangar. Good karma attracts good friends.
.
And with that, I will come to my point. If you are going to own an airplane, probably the best thing you can do is to maintain the best karma you can, because it affects how people treat you, whether they are going to help you or rip you off. I have been able to enjoy aviation at a very low and predictable overall costs because a lot of people along the way chose to help me rather than take advantage of me.
In aviation you have to guard your karma well.