I imagine you must be frustrated by this lawn situation. I've dealt with weeds in my lawn and know what it's like.
The presence of both clover and moss, besides being irritating, reveals something about your soil: It doesn't possess the ideal conditions to grow grass. Clover indicates low soil fertility. Moss indicates low fertility, low pH, poor drainage, compaction, or shade. Since you said you have sun, I suggest you begin dealing with this situation by getting a soil test. You can do this at your local county extension office. They'll give you test results AND recommendations of how to "fix" the soil so it's ideal for growing grass.
Meanwhile, as the soil is being tested, tackle the present crop of clover. You can spray it again, or, if it's manageable mow and/or dig it. If you mow, do this: Rake the stems hard, so they stand up. Mow low, so they chop off. Rake them and gather them, so they don't root. Then you can go after the crowns. Clover is hard to dig; it has deep roots, so if you want to spray it, go for it BEFORE mowing so there are plenty of leaves to take up the spray.
When the soil test results come back, amend your soil accordingly, and then reseed. That should do it!
To follow organic lawn practices, check out the company www.gardensalive.com . They carry lots of organic lawn care, and they have free info on their site. If you see a product there you like, try to source it locally if you can. I haven't been able to find what they have locally in Iowa, but I always try! It doesn't hurt to save some money on shipping...Their lawn care stuff is great. I recommend their WOW (without weeds) program for lawn care. It's wonderful.