First thing to do is outline the area you want in wildflowers only. Rent a sod cutter that takes out all grass and roots...turn over to store as compost or to make plant beds. Great stuff, don't get rid of it. Pile up on areas you'd like beds or areas you would like to kill weeds. Turn upside down and top with 4 inches of topsoil and lastly 2" of mulch. Dig a 6"x 6" trench along the defined edge of your lawn...this is for any beds made for ornamental plants, annuals, perennials I use trenches to define the edges between plant beds and lawn. Once you've made the beds with the sod then add the topsoil and then the mulch. Plant when you want. The height of the bed will reduce quickly. Pile as high as 2 feet which will flatten to less than a foot as the grass is decomposed. No worry of grass or weeds growing from beneath at least 2 inches of soil or mulch.
Back to your wildflower garden, wildflowers do look great with added pasture grasses. For the winter you weed wack down to 8" and the next spring, those flowers will have reseeded and the grasses will have out competed the weed weeds.
After removing the sod (2" thick) I'd simply rake the surface to loosen the soil. Throw meadow seeds and wildflower seeds by hand over the soil. It will look more natural if you do not mix thoroughly with the grass. Rake with the back of the rake (soft leaf rake not rock rake), water shallowly for 2 weeks keeping just the top inch of soil moist. When most of your plants reach 4 to 6" then start to water deeply and allowing to dry before watering again. Fertilizer, I'd just use OSMOCOTE extended release 14-14-14 after the starts are 4". Err on the light side and if possible, use a Scott's hand spreader. Shouldn't have to fertilize again until next spring.
Keep the seed bed moist, do not saturate. Do not allow to dry out until you've got 4 -6" of germinated grass/flowers above the soil. Then slowly allow to dry out more and more training your plants to develop deep roots.
Mow in the fall to the 6 " height. Or wait until spring, my favorite time to clean the garden. The dead plants are spreading seed and protecting the perennials by making mini greenhouses using the dead material. What is your zone and soil type?
Sod cutter, take out sod and keep it for plant beds or weedy places. Now, when your soil is dry dry dry because of your clay, rent a rototiller and 'fluff' up your soil in that area. Grade with a rake, rent a roller that you fill with water, compress all that fluffy soil. Spread your seed, take pieces of your sod turn over and shake to thinly cover seed. Roll again. OR, after rototilling, spread seed, rake with the back of the soft rake, then roll again to get good seed to soil contact. Fluffing up lawn bed soil should fill that 2" of sod you removed easily if not more. Why did I not see the measurements? This would actually be better for the seed and what you would like to achieve. An even cheaper, lazier way would be to rototill your area with the grass in place. Sounds as if that is what you did the last time. This time weed wack it all down to the ground, scalping the grass (here is where you could promote sweeps of grasses...the grass you want to keep don't scalp). Rototilling should be very easy without the long grass slowing the tines. Some of it will grow back, don't know what grasses are in your lawn but probably Fescue which will look great mixed with wildflowers AND you'll mow it down for the winter or in the spring. Won't be as thick with wildflowers but far cheaper. After spreading your seed, you should use the roller to get the soil seed contact. This should make that area raised above the lawn or adjoining areas a few inches in fact. I would probably chose to do the one removing the sod, rototilling, raking, seed, roll using pasture seed that is able to grow taller than lawn grass species and yet not get too dense to allow wildflowers to seed and get planted in soil for the next year. You'll probably need to reseed a bit the next spring. The rental for the roller will be $25 (estimate only), the rototiller for a whole day $75, the sodcutter for the entire day, $75. You can easily get the jobs done within 4 hours and return for even less unless they have minimums. We are up to $175 and your seed cost and shoot, I'd use good ole OSMOCOTE a one pound bottle costs $16 or less. Lightly spread...the beads might be too big for a hand spreader so spreading by hand is in order. Doing this on a lawn, fertilizing by hand will be very apparent, but not a wildflower bed. Try to shoot a density of 2 beads per sq. inch. It will be easier to do now than after germination. After your bed gets growing, 1 foot, you should thrown a bit more onto this bed. About the same amount you used to get 2 beads per square inch average. The first time you do this MEASURE the amount so that you can use the same amount the second time. See how this relates to the amount the directions tell you to use. Less is better but you have to have some fertilizer. The nitrogen is IN that sod you removed. Which is good to remove it as too much fertilizer will make your wildflowers luscious with leaves not flowers. OSMOCOTE 14-14-14 at even numbers will give just enough chemicals in the right proportion to promote reproductive growth, ie) flowers. This might be all that is needed for fertilizer for the entire season. Send a picture at the end of the season. One more fertilization might benefit your wildflower and grass bed to allow the perennials and grass more root growth during the winter. If stuff starts growing too early next spring, go get row cloth to cover the newbie plants at night. Cheap. Zone 3...perhaps weed wack the entire plot in late fall before frost, then cover with row cloth for the winter. That will help protect the more tender seeds as well as promote more root growth for the perennials. That debris you cut off will have a chance to begin to decompose. Just trying to help you to not have to repeat all this work. Have you purchased your wildflower seeds? Try to get them from growers in your zone...reputable seeds. Don't get them at the grocery store or home depot. Look for ZERO weed seeds or plants you don't want growing. A feed store will have different mixes of pasture grasses. Try to get ONE type of pasture seed. Throw this seed in 'sweeps' not evenly mixed with the wildflowers. I can explain more if these solutions fit your budget! That is a lot of topsoil that won't be necessary to buy! I love using machines, each of these machines should be easy peasy to do. I'd take out the sod myself but make sure you lower your mower or use a weed wacker first and take that vegetation down to the ground before cutting the sod. Rototilling the bare soil will be very different than the last time you rototilled! I am the laziest gardener in the world, I swear. These machines should be ENJOYABLE and confidence building to use!!