I'm a big fan of the attached
solar greenhouse. I've been living with seasonal attached greenhouses as our only source of heat for the past 20-some years in Ladakh, at high altitude with people ice skating outside.
But! But I'm at only 34N latitude, and 10,500 feet altitude (thin atmosphere above us), and in a desert with usually sunny dry winters, so our greenhouses get nice and warm even in January. But Minnesota is a lot further north, a lot lower, and maybe less sunny in winter. So your results will certainly vary.
I've seen that even dappled shade makes a big difference in the
solar heat gain in winter. Around here, snow evaporates (well, sublimates) by 9am wherever sun hits it, but in the dappled shade of leafless deciduous trees, it can sit on the ground for days.
I also was underwhelmed by the one underground greenhouse that we made. The southern side of the greenhouse shaded pretty far into the greenhouse, especially in mid-winter when the sun angle is low. We've had better results with having only slightly recessed beds in a ground level greenhouse, so we can cover seedlings with an extra layer on especially cold nights. However, I've seen convincing discussions about how a recessed greenhouse can be better in a place that doesn't get much solar gain in midwinter. Then again, if you will have heat tubes running under some of the beds, maybe that could replace the underground function.
I don't try to have a tropical climate in my greenhouse, I just extend my climate a couple of zones warmer. It does go below freezing for many nights between late Dec and early Feb, but certain greens and herbs don't mind, and others just kind of hunker down for the winter and resume growth in Feb when things warm up. It lets me keep perennials that might not survive outdoors, like certain herbs and flowers.
I love having the winter greenhouse attached to the house. I just love staggering out into it with my morning
coffee when there hasn't been any greenery outdoors for months, and doting on the latest seedlings and admiring my fresh greens and herbs. The flowers that bloom in the winter greenhouse get much more attention than any summer flower. Smells in the greenhouse can permeate the house, so you may find that you don't want to keep your compost inside the greenhouse after all -- but this sounds like something you can simply change if you don't like it.
15 x 20 feet sounds big enough to be worth it. Mine is 7 x 30 so it's a little smaller than yours; I'm not producing huge amounts from it, but the benefit to my mental state in winter is enormous -- fresh greens, basking in the sun, doodling with greenery, enjoying flowers, all round cheerful start to the morning. The cats love it too. I don't even use all the space in mine, since I have to haul the water by hand; I'd like to have more of the floor planted, but then it can cause moisture and condensation.
To learn more about growing food in the winter greenhouse, I keep going back to the Eliot Coleman
books, The Winter Harvest Handbook and The Four Season Harvest.