Many variants and many species. Not an easy answer. Why are you looking at clover as a possible planting? Where, and why?

What I would do is to fertilize only the St Augustine. Mow at the highest setting and allow the St Aug to go 2 weeks. Water deep and infrequent like we talk about and "favor" the St Aug. Your grass in the shade will need water less often than the grass out in the full sun. Don't water when the crabgrass looks dry. Water when the St Aug out in the sun looks dry. The shady grass will appreciate it, and it still won't encourage weeds. Crabgrass is a summer annual plant that thrives in the heat and full sun. With your lot size it's going to take a year or so for the St Augustine to completely grow out and take over. If you wanted to speed up that process, put a couple pieces of St Aug sod around amongst the weeds and do the 1,2,3 above. As the runners spread out, you have to fertilize along the runners, too. I use organics to fertilize so I'm not at all worried about over applying fertilizer. If you have access to the Floratam variety of St Augustine, use that out in the sun. If you want to use a spray weed killer, you cannot use normal Weed-B-Gone with 2,4-d in it. You have to use atrazine. Everything else seems to kill St Augustine. Here's one you can get at Walmart. Read the directions carefully. This stuff is not to be trifled with. You have to walk backwards as you spray so you don't walk through the wet grass. That makes planning your route slightly more important. Don't paint yourself into a corner where you can't get out. And you can only spray it twice in a year, so choose your timing wisely. Remember you are only wetting the weeds, not drenching the soil with it. It can take 2 weeks before you see the first signs of the weeds dieing, but "suddenly" they'll all be dieing. All you need to spray is around the St Augustine runners. I would leave the rest of the weeds to grow until the St Augustine spreads to fill it all in. When you spray around the runners, that kills the weeds around the runners giving them more light and soil to expand into. And you don't need to spray in the middle of the dense St Augustine except where you have the clovery stuff growing. Once it gets pretty dense it fights off the weeds by itself. Also rather than connecting a bottle like that directly to a hose I connect through another nozzle with a valve so I can turn the flow on and off. Those are cheap at Home Depot or Lowe's. Here's a link to a picture. Cheap hose-end valve.

"This is not a likely option because of the amount of area that my baby tears covers." It can feel daunting at the outset when the vista of work spread out before you seems like a bottomless pit, yes. But you simply start at one end and try to get into the zen of it and before you know it you have gotten a fair sized patch done. Repeat the next day and so on. Devote an hour a day and you'll be surprised what you can accomplish. Actually, weeding is kind of one of my most favorite things to do. It is of course tedious but the results are instant and very rewarding.

Everything I read said that the day temp needs to be 65-70, but today is 73! I've been waiting for it to be a tad cooler. This weekend was the plan, though. I've been using Round Up, but didn't want to kill the K31 that's sprouting. I figure, if it's trying THAT hard in a shady area then I should let it be! LOL