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.

In Oklahoma a lot of people want to live on acreage. Also for reasons that escape me they love to mow. It does look nice afterwards but spending hours that way is not my choice. But what people on acreage generally do is not worry about what is growing in the "lawn " and just mow it regularly. Green is green and we have droughts. People in the country do not generally water unless they have one of those septic tanks systems which also converts to irrigation in that area. They generally mow a large area around the house-at least an acre. because also there is fire danger and long, shaggy, dry vegetation is dangerous and also there are rattlers and copperheads and no one wants to be surprised so close to the porch. Depending upon where you live there can be safety concerns with not mowing. That said letting the remaining acres revert to wild flowers and cover for wildlife is lovely. Down the line if someone want to buy acreage you will see as many people who like a meadow or a horse pasture as like a vast, expensive lawn. It is also a service to the birds and insects not to use lawn chemicals. I have deliberately inter-seeded clover in my city backyard. I have a giant oak at the center of the yard and grass has a hard time maintaining under it. Clover does not maintain well once it is consistently in the 90's either but is lovely in the spring when the grass is just getting going. Some of my neighbors probably wish I had the more consistent weed free carpet but it cannot be done without heavy chemical use. I think we should minimize that.

Hmm, Desmodium paniculatum (Panicled Tickclover) does look like a good match, thanks!!

Creeping red fescue struggles in high-traffic areas, is highly susceptible to summer dormancy or heat-induced browning, and suffers in waterlogged or heavily compacted soils. While excellent for shade and low-maintenance lawns, its very fine, soft blades can also flop over if mowed too tall. A breakdown of its main disadvantages includes: 1. Poor Traffic Tolerance Wear & Tear: It has moderate to low wear tolerance. Heavy foot traffic, pets, or constant use can quickly damage and thin out the turf. Slow Recovery: Unlike self-repairing grasses like Kentucky Bluegrass, its lateral spread is relatively slow, meaning it struggles to recover from damage on its own. 2. Heat & Drought Vulnerability Summer Dormancy: In regions with prolonged heat or full, direct sun, creeping red fescue tends to go dormant quickly, turning brown. Not for the Transition Zone: It will struggle in hot, humid climates and is best reserved for cooler northern regions or deep shade. 3. Moisture & Soil Issues Waterlogged Soils: It is highly intolerant of poorly draining soils or standing water. Compaction: Creeping red fescue roots are shallow compared to other turf types and perform poorly in hard, highly compacted earth. 4. Maintenance & Mowing Quirks Mowing Difficulty: Because the leaf blades are extremely fine and soft, they have a tendency to "lay down" or fold over if allowed to grow too tall, which can make a clean cut very difficult. Thatch Build-Up: Over time, it can accumulate heavy thatch that requires regular maintenance to manage. 5. Disease Susceptibility When grown in full sun or overly wet conditions, it is highly prone to fungal diseases such as red thread, leaf spot, and dollar spot.