Reddit mentions of The Know Maintenance Perennial Garden

Try some plants...hostas, huechera, there are many options for shade plants. Define a garden area and fix your lawn.

Edit: Carex is another good one

Edit2: Just buy this book and follow the directions to put in a shade garden: https://www.amazon.com/Know-Maintenance-Perennial-Garden/dp/1604693347/ref=sr_1_1/132-0664672-7234612

Not an English-style cottage garden, but the New Perennialist style might satisfy your requirements. Start with this blog post about native (Eastern US) plants for a cottage garden, and this one about selecting plants for smaller gardens. For practical guidance, plant varieties, and sample designs, see The Know-Maintenance Perennial Garden, by Roy Diblik.

Maybe we just need a closer picture. I would say do it in sections and when you weed it, plant more low maintenance flowers that go with the style that is there now. Echinacea, rudbeckia, golden alexanders, alliums, columbines and phlox would all look great there. Prairie plants will suffocate weeds after a few years. This book is the best I've read on low maintenance landscaping: Know Maintenance Perennial Gardening and it's got great recommendations for the midwest. You will still need to do some weeding (and probably a lot to begin with) but if you get a dutch hoe like he recommends it doesn't take long and I personally enjoy it. You have a great start already with some healthy looking flowers there already. Mixing in some tall grasses can be cool if you just want to take up some space. Wild geraniums would look awesome on the front border.