The AG one I'd do, they got a code 1056 for wildlife foodplots. Focus is pH, CEC. Seeing phophorous or pottasium isn't that bad. IF one is quite low, maybe level out while soil pH improves over time.
IF you're doing bags of lime, you probably wont put out as much as they ask for. Predominate weeds is a major sign of your soil. I did dairyone's lab in NY for apple tree site prep. They told me 5 tons per acre.... 2 tons per acre on that .4 acre plot is going to be. 1600lbs. That's (40) 40lb bags of pelletized lime if it's 100% calcium equivalent, which its not. PRobably more like 45-50 bags to get that number.
Most clay soil take 2 tons per acre to raise the pH by 1. That's assuming 6 inches of tillage depth. Often no-till is 1/2 ton / acre per year.
You might be better off renting a tow behind spreader. Usually 2-4 ton capacity.
Buying (40) 50lb bags of barn lime is $200 plus tax. Buying (50) 40lb bags of pelletizd lime is $350 plus tax. tractor supply vs home depot. Getting a tow behind drop spreader can pay for itself quickly. Buying it in bulk will get you at your target much more feasibly. Might find someone with a pickup truk dump or tow behind dump trailer for a reasonable price.